Strongly correlated stochastic systems

Marco Biroli

REVIEW 2 major objections 5 minor 196 references

Strongly correlated stochastic systems

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Conditionally independent identically distributed random variables—variables that become independent when a hidden parameter is fixed—admit exact universal formulas for extremes, order statistics, gaps, and particle counts, and these…

desk verdict A coherent thesis that turns conditionally independent variables into universal large-N formulas for resetting systems; the core is solid, but the first-passage edge statistics rest on an unvalidated saddle point and the atomic-spacing result is a one-parameter fit. read the letter →

arxiv 2508.12818 v1 pith:AOZ62GZQ submitted 2025-08-18 cond-mat.stat-mech

Marco Biroli This is my paper · ORCID

classification cond-mat.stat-mech

keywords stochasticprocessesnon-equilibriumsteadystatesextremevaluestatisticsstrongcorrelationsrandommatrixtheorysearchconditionallyindependentvariablesresetting

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This thesis develops exact analytical tools for strongly correlated stochastic systems, where many particles move together and cannot be treated as independent. Its central object is a family of random variables called conditionally independent identically distributed (CIID) variables: the variables become fully independent once a small set of latent parameters is fixed, even though their marginal joint distribution is strongly correlated. The thesis proves that, in the large-$N$ limit, the center of mass, order statistics, extreme values, gaps, and full counting statistics of such variables all have universal closed-form expressions written in terms of the conditional distribution and the law of the latent parameter. The same renewal structure appears in non-equilibrium steady states created by simultaneous stochastic resetting, so the formalism yields exact results for gases of resetting Brownian motions, ballistic particles, and Lévy flights, and it explains the emergent conditional independence seen in a switching harmonic trap that matches experiment. The payoff is that strong correlations, usually a source of intractability, become a route to new universal laws.

What carries the argument

The central object is the family of conditionally independent identically distributed (CIID) random variables, defined by a joint distribution that factorizes once a latent vector $\vec{Y}$ is conditioned upon: $P(\vec{x})=\int d\vec{y}\,h(\vec{y})\prod_i p(x_i|\vec{y})$. The quantitative work is done by the fact that, for large $N$, the conditional observables are sharply peaked—except when the conditional tail is of Fréchet type—so the latent variable acts as a selector of the quantile, the gap scale, or the counting fraction; the final, correlated statistics are then a weighted average over $h(\vec{y})$. This machinery converts the intractable question of strongly correlated statistics into a one-dimensional (or low-dimensional) integral over the hidden parameter.

What would settle it

Simulate the first-passage resetting model with a large number $N$ of diffusive particles that all reset whenever any one reaches a boundary at $L$; measure the steady-state density width and the distribution of the maximum. If the density does not shrink as $L/\sqrt{\log N}$ or $M_{1,N}$ is not uniformly distributed on $[0,L]$ in the large-$N$ limit, the saddle-point derivation collapses, showing that the CIID structure does not extend to this first-passage protocol.

Watch

Extended reading notes

Core claim

The central claim is that conditionally independent identically distributed random variables, with joint density $$\int d\vec{y}\,h(\vec{y})\prod_{i=1}^{N} p(x_i|\vec{y}),$$ obey exact universal large-$N$ statistics that mirror the classical theory for independent variables. In the bulk, the $k=\alpha N$ order statistic concentrates on the $\alpha$-quantile $q(\alpha,\vec{y})$ of the conditional distribution, with probability density $\int d\vec{y}\,h(\vec{y})\,\delta[w-q(\alpha,\vec{y})]$. The extreme-value statistics inherit the tail class of $p(x|\vec{y})$; for Gumbel and Weibull tails the bulk formula extends to the edge, whereas for Fréchet tails the edge statistics require a separate scaling form. Gap statistics and full counting statistics acquire analogous closed expressions, and applied to simultaneous resetting this yields exact steady-state densities, extreme-value laws, and counting distributions for Brownian, ballistic, and Lévy gases.

Load-bearing premise

The derivation of the steady-state joint distribution for the first-passage resetting model (Section 8.2.4) rests on a crude Laplace saddle-point approximation (Eqs. 8.120–8.121) that must be uniformly valid in the large-$N$ limit; if it fails, the predicted condensation of particles near the origin and all derived observables for that model would be unsupported.

Editorial extensions

If this is right

In any physical system whose steady state admits the CIID form, the bulk order statistics are completely determined by the quantile of the conditional distribution; for a simultaneously resetting Brownian gas this gives $M_{k,N}\sim \sqrt{4D/r}\,\mathrm{erfc}^{-1}(2\alpha)$ and a universal scaling function $f(z)=2ze^{-z^2}$ for all edge order statistics.
For ballistic particles resetting to the origin, the particle density involves an exponential integral, the maximum is exponentially distributed, and the bulk gap distribution is $rN K_0(\sqrt{2rNg})$, showing a stretched-exponential tail with exponent $1/2$.
For Lévy flights with simultaneous resetting, the bulk order statistics follow the scaling law $f_\mu(z)=\mu z^{\mu-1}e^{-z^{\mu}}$, while the maximum has a different scaling $S_\mu(z)=\mu z^{\mu-1}/(1+z^{\mu})$; the first gap grows as $N^{1/\mu}$, a signature of the dominance of extreme events.
In the first-passage resetting model (all particles reset whenever any one reaches a target), the gas condenses on a scale $L/\sqrt{\log N}$ while the maximum is uniformly distributed on $[0,L]$, meaning the system operates perpetually on the edge of resetting.
For search processes, resetting lowers the mean first-passage time only up to a small number of walkers—independent resetting helps for $N\le 7$, simultaneous resetting for $N\le 6$—and beyond these thresholds resetting hinders the search.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The quantile-concentration mechanism suggests a general recipe: any mechanism that introduces a slowly fluctuating global parameter—trap stiffness, diffusion coefficient, or experimental calibration error—should imprint all-to-all correlations whose extreme, gap, and counting statistics are computable from a single integrating variable. This could be tested directly in optically trapped colloids w
Because bulk order statistics collapse onto the conditional quantile, recording the position of the $\alpha N$-th particle over many experimental runs directly reveals the distribution of the latent parameter; this offers a non-invasive way to infer hidden environmental variability from extremal data alone.
The linear maximum law predicted for the first-passage resetting gas, if confirmed at large $N$, implies the system is always 'critical'—most particles hug the origin while a rare walker hits the target. A natural extension would test whether this behavior persists with a soft absorbing layer, in higher dimensions, or with interacting particles.
The same quantile mechanism likely applies to 'diffusing diffusivity' models, where a fluctuating diffusion coefficient acts as the latent variable; the thesis's results then predict that extreme and gap statistics in such heterogeneous media are universal and exactly computable.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This is a thesis that deserves referee time. The central contribution is real: a general formalism for conditionally independent identically distributed variables, with universal large-N formulas for the sum, order statistics, extremes, gaps and full counting statistics, plus a catalog of physical systems where the structure emerges — simultaneous resetting, switching harmonic traps, and resetting Dyson Brownian motion. The mixture/superstatistical idea is not new, and the paper credits the relevant literature. What is new is the systematic exact limit theory and the demonstration that diverse resetting steady states fall into this framework. Chapter 7 is a clean and honest derivation: it is conditioning plus classical iid results, and the tail classification into Gumbel, Weibull and Fréchet cases is done carefully. The applications in Chapter 8 are also well executed, and the numerical comparisons in the published parts of the thesis are genuinely supportive. The switching-trap experimental comparison in Chapter 9 is a real plus: theory and experiment matching for order statistics, gaps and FCS is exactly the kind of evidence that raises confidence.

The soft spots are localized. First, the unpublished first-passage resetting section (8.2.4) derives the steady-state conditionally independent form through a 'crude Laplace saddle-point' approximation (Eqs. 8.120–8.121) for which I could not find a uniform error estimate. The replacement of killed Brownian densities by free Gaussians is not uniform near the absorbing boundary at L, and the edge maximum law (Eq. 8.132) and edge gaps are precisely the observables controlled by that boundary behavior. The paper does not show numerical checks of the triangular maximum law or edge gaps. The bulk density, bulk order statistics, bulk gaps and FCS are checked and agree, so the model as a whole is probably right, but the edge claims in this section need an independent numerical check before being cited. Second, the atomic-spacing fit in Chapter 10 uses gamma = mu/r = 0.31 as a fitted parameter; that is a fit, not a prediction, and the wording should be careful there. Neither soft spot undermines the central CIID formalism, which stands on its own.

The citation pattern is honest: it acknowledges superstatistics and prior resetting work rather than hiding them. The paper also flags the saddle point as crude, which is the right instinct. For a reader working on resetting, extreme statistics, or exactly solvable non-equilibrium states, this is a very useful collection. I would send it to peer review, with a request that the first-passage edge statistics be checked numerically and the atomic-spacing fit discussion be softened.

Referee Report

2 major / 5 minor

Summary. This PhD-thesis manuscript develops a general formalism for random variables that are independent and identically distributed when conditioned on latent variables (CIID variables) and derives universal large-N asymptotic results for their center of mass, order statistics, extremes, gaps, and full counting statistics. It then applies this formalism to several multiparticle systems: simultaneously resetting Brownian gases, ballistic gases, Lévy flights, a switching harmonic trap, a first-passage-resetting gas of Brownian particles, and a resetting Dyson log-gas. The central Chapter 7 derivations are clean consequences of conditioning plus classical iid results, and the resetting applications in Sections 8.2.1-8.2.3 follow from exact or well-defined renewal/Fokker-Planck structures. Many predictions are compared with simulations, and the switching-trap results are compared with experiments. The main unverified point is in Section 8.2.4, where the exact steady state for first-passage resetting is replaced by a 'crude' saddle-point approximation without a uniform error estimate; the edge maximum law obtained from that approximation is not numerically tested.

Significance. If the program is accepted, the CIID formalism is a significant contribution: it provides a unified, analytically tractable family of strongly correlated systems for which bulk and edge observables admit closed-form scaling functions, and it gives a mechanism—stochastic resetting—that generates such correlations. The paper's strengths are its clean derivations of the universal results from conditioning, the nontrivial scaling functions for gap statistics and full counting statistics, the experimentally supported switching-trap results, and the search-optimization applications. The exactness claims are mostly carefully qualified; the principal exception is the first-passage-resetting chapter, where a load-bearing approximation is left unchecked.

major comments (2)

[§8.2.4, Eqs. (8.120)-(8.121) and (8.132)] The exact steady state in Eq. (8.120) is an average over the last-passage time t of products of killed Brownian densities p≤L(x_i,t), each of which vanishes at x_i=L. The transition to Eq. (8.121) replaces these killed densities by free Gaussian kernels, which do not vanish at the absorbing boundary. This replacement is not uniform in x: near x=L the image term cancels the Gaussian term exactly, and the maximum M_{1,N} and the order-one edge gaps are controlled precisely by particles near x=L in the latent-t tail. Consequently the 'stuck to the hard edge' condensation picture and the triangular law Prob[M_{1,N}=w]=2w/L^2 in Eq. (8.132) are not protected by the CIID formalism of Chapter 7 and inherit whatever error the saddle-point approximation makes. The paper itself labels the step 'crude' and supplies no error estimate, and the numerical checks in Figs. 8.19-8.20 are for the density, bulk order statistics, bulk gaps, and full counting statistics, not for the edge maximum or edge gaps. Please either provide a controlled asymptotic derivation of Eq. (8.121) from Eq. (8.120), or add a direct numerical test of Eq. (8.132) and the adjacent edge gaps, and revise the claims accordingly.
[§5.7 and Fig. 5.8] The comparison of the resetting Dyson gas spacing distribution with atomic level spacings uses gamma=mu/r=0.31, which is chosen to fit the data. Since gamma is a free parameter of the model and is not fixed by independent physical input, the statement that the model can 'fit atomic spacings that could not be described by the Wigner surmise' is a one-parameter fit claim rather than a parameter-free prediction. Please report the fit procedure, the spread of the data around the fitted curve, and the sensitivity of the fit to gamma, or identify independent evidence that fixes gamma.

minor comments (5)

[Eq. (8.111) (also Eq. (6.78))] In the method-of-images expression, the second exponent is written as e^{-(x-2z)^2/(4Dt)}; the boundary location is L, so this should read e^{-(x-2L)^2/(4Dt)}.
[§8.2.3, Eqs. (8.79)-(8.80)] The Lévy flight propagator is a large-time asymptotic form, so Eq. (8.80) and the resulting steady-state results are asymptotic in the scaling limit rather than exact for finite N; please state this qualification explicitly in the main text and in the summary figure Fig. 5.5.
[Fig. 5.7 and §9.3] The experimental comparison would be more convincing with error bars and a precise statement of how the one-dimensional samples are extracted from the two-dimensional trajectories; the word 'perfectly' overstates the agreement visible in the figure.
[General, numerical sections] The simulation figures report very large N but not run lengths, numbers of independent samples, or error bars; reporting these would allow the claimed 'excellent agreement' to be assessed quantitatively and would improve reproducibility.
[§5.8 and §11.2] The summary states critical walker numbers N≤7 and N≤6 without defining Protocols A and B; please refer explicitly to the corresponding subsections of Chapter 11, or define the protocols in the summary.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: CIID results follow from the mixture definition and resetting models from explicit renewal dynamics; the crude saddle-point approximation in Sec. 8.2.4 is a correctness risk, not a circular step.

full rationale

The derivation chain is self-contained. Chapter 7 defines CIID variables by Eq. (7.5), Prob[X = x] = ∫ d^M y h(y) ∏ p(x_i|y). For fixed y the variables are i.i.d., so the standard i.i.d. results of Chapter 6 apply conditionally; averaging over h(y) gives the mixture formulas (7.25), (7.36), (7.71), and (7.83). This is a direct mathematical consequence of the definition, not an input disguised as an output. The resetting models are independent inputs: the steady states (8.30), (8.53), (8.80), and (8.121) are obtained from renewal equations of the stated dynamics, then inserted into the CIID formulas; no observable is fitted to produce the predicted distributions. The log-gas atomic-spacing comparison (Fig. 5.8) is explicitly a fit with gamma = 0.31, not a prediction. The self-citations [1]-[6] are to papers whose derivations are reproduced in the thesis; no load-bearing external uniqueness theorem is imported. The one flagged weakness is Sec. 8.2.4: Eq. (8.120) is converted to Eq. (8.121) by a 'crude Laplace saddle-point approximation' with no uniform error estimate; the paper itself labels it crude, and the edge maximum law (8.132) is therefore at risk. That is a correctness/rigor concern, not a circular reduction, because the output is not equal to the input by construction. Hence no circularity steps and score 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The framework rests on the conditional-mixture representation of the joint distribution, the tail classifications of conditional densities, and the renewal/Fokker-Planck derivations that produce the mixing distributions. The single free parameter appears in the atomic-spacing application, not the core formalism.

free parameters (1)

gamma = mu/r in Dyson Brownian motion spacing fit = 0.31
Used in Fig. 5.8 to fit atomic level spacing data for ten elements; tunes the competition between the harmonic trap and resetting, and is not predicted by the model.

assumptions (5)

domain assumption Brownian motion propagator and Markov property
Used throughout (Sec. 6.3, 8.1) to write reset-free segment propagators and renewal equations.
domain assumption Lévy stable law tail approximation p0(x,t) ~ G tau / x^(1+mu)
Used in Eq. (8.93) for Lévy flight extremes; standard asymptotic for stable laws.
domain assumption Renewal equation for simultaneous resetting
Eq. (8.25) encodes the reset process; assumes all particles reset at common Poisson times and evolve independently between resets.
ad hoc to paper Saddle-point approximation in first-passage resetting
Eqs. (8.120)-(8.121) use a 'crude Laplace saddle-point approximation' to obtain the h(u)=2/u^3 structure.
standard math Tail classification of conditional distributions into Gumbel, Weibull, Fréchet classes
Used in Sec. 7.3 to distinguish concentration cases for edge order statistics; standard extreme value theory.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Strongly correlated stochastic systems." pith.science (2026). https://pith.science/paper/AOZ62GZQ

@misc{pith2026250812818,
  author       = {Pith},
  title        = {Pith review of: Strongly correlated stochastic systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AOZ62GZQ}},
  note         = {Machine review of arXiv:2508.12818}
}

read the original abstract

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the universal characterization of conditionally independent identically distributed variables-random variables that become independent upon conditioning on latent parameters. This structure arises naturally in systems with stochastic resetting, a mechanism that generates strong long-range correlations while retaining analytical tractability. Using this framework, we derive universal closed-form expressions for several observables across diverse models, including Brownian motion, Levy flights, ballistic particles, and Dyson Brownian motion, under various resetting protocols. In particular, we demonstrate that resetting induces analytically tractable non-equilibrium steady states. Theoretical predictions are supported by numerical comparisons and experimental comparisons in systems such as diffusive particles in switching harmonic traps. Applications to search optimization are also explored, identifying regimes where resetting enhances or impairs first-passage efficiency, and proposing rescaling-based protocols that outperform traditional resetting.

Figures

Figures reproduced from arXiv: 2508.12818 by the authors.

**Figure 5.1.** A visual representation of the main observables studied in the the [PITH_FULL_IMAGE:figures/full_fig_p021_5_1.png] view at source ↗

**Figure 5.2.** A summary of the behavior of some key observables of a gas of Brownian motions. Unlike all the resetting processes, free Brownian motion does not admit a stationary state at long times. To obtain static distributions as shown in the figure we have to rescale particle positions by √ 2Dt. The scaled average density profile is plotted with a black line. The distribution of the position M1,N of the rightmost particle is… view at source ↗

**Figure 5.3.** A summary of the behavior of some key observables in the non [PITH_FULL_IMAGE:figures/full_fig_p025_5_3.png] view at source ↗

Figures from the paper (58 more)

**Figure 5.4.** Figure 5.4: A summary of the behavior of some key observables in the non [PITH_FULL_IMAGE:figures/full_fig_p025_5_4.png]

**Figure 5.5.** Figure 5.5: A summary of the behavior of some key observables in the non [PITH_FULL_IMAGE:figures/full_fig_p027_5_5.png]

**Figure 5.6.** Figure 5.6: A summary of the behavior of some key observables in the non [PITH_FULL_IMAGE:figures/full_fig_p028_5_6.png]

**Figure 5.7.** Figure 5.7: The experimental measurements for the distribution of the max [PITH_FULL_IMAGE:figures/full_fig_p029_5_7.png]

**Figure 5.8.** Figure 5.8: Experimental data (obtained from the Atomic Spectral Database [PITH_FULL_IMAGE:figures/full_fig_p031_5_8.png]

**Figure 6.1.** Figure 6.1: We recall here [PITH_FULL_IMAGE:figures/full_fig_p034_6_1.png]

**Figure 6.2.** Figure 6.2: A plot of the Gumbel, Fréchet and Weibull universal [PITH_FULL_IMAGE:figures/full_fig_p037_6_2.png]

**Figure 6.3.** Figure 6.3: A sketch of weakly correlated variables {X1, · · · , XN } split in M nearly independent blocks B1, · · · , BM. Variables within each block have correlations of order O(1) but correlations across blocks (represented by faded springs) are vanishingly small. The maximu…

**Figure 6.4.** Figure 6.4: A sketch of a one-dimensional Brownian motion and the geomet [PITH_FULL_IMAGE:figures/full_fig_p047_6_4.png]

**Figure 6.5.** Figure 6.5: A plot of the Gumbel, Fréchet, Weibull universal extreme-value statistics GI(z), GII(z), GIII(z) compared to the extreme-value statistics Q(z, t) of Brownian motion. The cumulative distributions Gρ(z) and Q(z, t) are shown on the left, and their derivatives, i.e. the…

**Figure 6.6.** Figure 6.6: Sketch of the blocking argument used to compute the maximum [PITH_FULL_IMAGE:figures/full_fig_p051_6_6.png]

**Figure 8.1.** Figure 8.1: A schematic representation of a one-dimensional resetting Brow [PITH_FULL_IMAGE:figures/full_fig_p070_8_1.png]

**Figure 8.2.** Figure 8.2: Left. A plot of the probability density function p NESS r (x) given in Eq. (8.6) of finding a resetting Brownian motion at x in the long-time limit once the non-equilibrium steady state has been reached. The plot was obtained with p r/D = 1. Right. A plot of the mean…

**Figure 8.3.** Figure 8.3: Schematic trajectories of N = 3 Brownian motions undergoing simultaneous resetting to the origin at random times. The observation time is marked by t and the time of the last reset before t is marked by t − τ . During the last period τ , the particles evolve independ…

**Figure 8.4.** Figure 8.4: A schematic representation of the position of the particles in the [PITH_FULL_IMAGE:figures/full_fig_p079_8_4.png]

**Figure 8.5.** Figure 8.5: Plots of the probability density functions of the center of mass (left [PITH_FULL_IMAGE:figures/full_fig_p080_8_5.png]

**Figure 8.6.** Figure 8.6: Plots of the probability density functions of the gaps (left panel) and [PITH_FULL_IMAGE:figures/full_fig_p082_8_6.png]

**Figure 8.7.** Figure 8.7: Schematic trajectories of N = 3 ballistic particles undergoing simultaneous resetting to the origin at random times. The observation time is marked by t and the time of the last reset before t is marked by t − τ . During the last period τ , the particles evolve inde…

**Figure 8.8.** Figure 8.8: A schematic representation of the position of the particles in the si [PITH_FULL_IMAGE:figures/full_fig_p085_8_8.png]

**Figure 8.9.** Figure 8.9: Left: The scaled distribution of the center of mass. The black line denotes the analytical scaling function ℓ(z) in Eq. 8.61 and the points represent numerical simulations. Right: The distribution of the k-th maximum Mk=αN,N in the bulk, given in Eq. 8.67, is plotte…

**Figure 8.10.** Figure 8.10: Plots of the probability density functions of the gaps (left panel) [PITH_FULL_IMAGE:figures/full_fig_p088_8_10.png]

**Figure 8.11.** Figure 8.11: Schematic trajectories of N = 3 Lévy flights undergoing simultaneous resetting to the origin at random times. The observation time is marked by t and the time of the last reset before t is marked by t − τ . During the last period τ , the particles evolve independen…

**Figure 8.12.** Figure 8.12: A schematic representation of the position of the particles for [PITH_FULL_IMAGE:figures/full_fig_p090_8_12.png]

**Figure 8.13.** Figure 8.13: The p.d.f. of the center of mass P(C, N) in Eq. 8.88 is shown by dashed lines for N = 1000 and for µ = 1.5, 1, 0.5 in the left, middle and right panel respectively. The dots represent numerical simulations. The center of mass We now turn our attention to the center …

**Figure 8.14.** Figure 8.14: The probability density function of the k-th maximum in the bulk Mk=αN,N in Eqs. 8.91 and 8.92 is shown for µ = 1.5, 1, 0.5 in the left, middle and right panels respectively. Different colors and symbols correspond to different values of k. The dashed black line co…

**Figure 8.15.** Figure 8.15: The probability density functions of the first, second and the third [PITH_FULL_IMAGE:figures/full_fig_p095_8_15.png]

**Figure 8.16.** Figure 8.16: Plots of the probability density functions of the gaps in the bulk [PITH_FULL_IMAGE:figures/full_fig_p095_8_16.png]

**Figure 8.17.** Figure 8.17: A sketch of the first-passage resetting model with N = 3 particles and a defect located at L > 0. Whenever any of the particles reach the defect all the particles reset to the origin. ρ(x, N|r) x 0 L O(√ L log N ) ∼ ∼ O(1) M1,N ∼ O(L) dN,N ∼ O( 1 N log N ) dαN,N ∼ O…

**Figure 8.18.** Figure 8.18: A schematic representation of the position of the particles in the [PITH_FULL_IMAGE:figures/full_fig_p097_8_18.png]

**Figure 8.19.** Figure 8.19: Left: The scaled average density of particles in the nonequilibrium steady state. The black line denotes the analytical scaling function ρS(z) in Eq. 8.126 and the points represent numerical simulations. Right: The distribution of the k-th maximum Mk=αN,N , given …

**Figure 8.20.** Figure 8.20: Plots of the probability density functions of the gaps (left panel) [PITH_FULL_IMAGE:figures/full_fig_p103_8_20.png]

**Figure 9.1.** Figure 9.1: A sketch of the optical trap experimental setup. The potential of [PITH_FULL_IMAGE:figures/full_fig_p106_9_1.png]

**Figure 9.2.** Figure 9.2: The stiffness of the confining potential is a two state system with [PITH_FULL_IMAGE:figures/full_fig_p107_9_2.png]

**Figure 9.3.** Figure 9.3: A sketch of the experimental setup. Four colloidal particles a placed at the vertices of a square. Using a laser we create four harmonic traps confining the particles close to their respective vertex. At random Poissonianly distributed times we switch the stiffness …

**Figure 9.4.** Figure 9.4: A recall of [PITH_FULL_IMAGE:figures/full_fig_p113_9_4.png]

**Figure 9.5.** Figure 9.5: Scaling collapse of the distribution of the [PITH_FULL_IMAGE:figures/full_fig_p115_9_5.png]

**Figure 9.6.** Figure 9.6: Scaling collapse of the distribution of the [PITH_FULL_IMAGE:figures/full_fig_p118_9_6.png]

**Figure 9.7.** Figure 9.7: Scaling collapse of the distribution of the number of particles [PITH_FULL_IMAGE:figures/full_fig_p119_9_7.png]

**Figure 10.1.** Figure 10.1: Experimental data (obtained from the Atomic Spectral Database [PITH_FULL_IMAGE:figures/full_fig_p130_10_1.png]

**Figure 10.2.** Figure 10.2: A schematic representation of the positions of the particles in the [PITH_FULL_IMAGE:figures/full_fig_p133_10_2.png]

**Figure 10.3.** Figure 10.3: A schematic representation of the positions of the particles for [PITH_FULL_IMAGE:figures/full_fig_p135_10_3.png]

**Figure 10.4.** Figure 10.4: Left. Plot of the scaling function ρS(z, γ) given in Eq. (10.42) vs the rescaled length z = x p µ/(ND), describing the average density profile of the Resetting Dyson Brownian motion in the non-equilibrium steady state. The lines are the analytical prediction given b…

**Figure 10.5.** Figure 10.5: Left. Plot of the scaling function g(z, γ) defined in Eq. (10.54) vs the rescaled maximum z = xmaxp µ/(ND), describing the probability distribution function of xmax representing the position of the rightmost particle of the Resetting Dyson Brownian motion in its no…

**Figure 10.6.** Figure 10.6: Left panel: Plot of Prob.[¯s|r] in Eq. (10.67) as a function of the scaled distance s C¯ (γ) with C(γ) given in Eq. (10.68) and the scaling function Fβ(u, γ) given in Eq. (10.63) describing the probability density of the gap of the β-Resetting Dyson Brownian motion …

**Figure 10.7.** Figure 10.7: Experimental data (obtained from the Atomic Spectral Database [PITH_FULL_IMAGE:figures/full_fig_p149_10_7.png]

**Figure 10.8.** Figure 10.8: Plot of the function G(v) given in Eq. (10.84). For a given κ, one can then read off v⋆ such that G(v⋆) = κ as stated in Eq. (10.91). The lowest allowed value κmin is given in Eq. (10.90). appears inside the variance σ 2 (τ ) = D(1 − e −2µτ )/µ. This full counting s…

**Figure 10.9.** Figure 10.9: Plot of the scaling function q(κ, ℓ, γ) vs κ given in Eq. (10.92) describing the full counting statistics, i.e., the probability density function of the number of particles in the interval [−L, L]. In this plot, we only show the smooth part of the scaling function …

**Figure 11.1.** Figure 11.1: A sketch of how resetting influences a general search process. [PITH_FULL_IMAGE:figures/full_fig_p156_11_1.png]

**Figure 11.2.** Figure 11.2: Typical trajectories for N = 3 one-dimensional random walkers undergoing independent resetting (protocol A) in the left panel and simultaneous resetting (protocol B) in the right panel. Different colors correspond to different walkers and the resetting events are s…

**Figure 11.3.** Figure 11.3: Comparison of theoretical and numerical Langevin results for the [PITH_FULL_IMAGE:figures/full_fig_p163_11_3.png]

**Figure 11.4.** Figure 11.4: The derivative of the mean first passage time at [PITH_FULL_IMAGE:figures/full_fig_p166_11_4.png]

**Figure 12.1.** Figure 12.1: Schematic trajectories of a rescaling random walk, as defined in [PITH_FULL_IMAGE:figures/full_fig_p169_12_1.png]

**Figure 12.2.** Figure 12.2: Plot of the steady-state probability density [PITH_FULL_IMAGE:figures/full_fig_p170_12_2.png]

**Figure 12.3.** Figure 12.3: The dimensionless mean first passage time [PITH_FULL_IMAGE:figures/full_fig_p176_12_3.png]

**Figure 12.4.** Figure 12.4: Left: The optimal value ℓ ∗ (a), at which T˜(0) achieves its minimum as a function of ℓ for a fixed a, plotted as a function of a for 0 ≤ a < 1. Right: The optimal mean first passage time Topt(a), i.e., T˜(0) evaluated at ℓ = ℓ ∗ (a), plotted as a function of 0 ≤ a …

**Figure 12.5.** Figure 12.5: For −1 < a ≤ 0, the nonlocal differential equation (12.52) needs to be solved in different segments that are interconnected. The segment I denotes the region x ∈ [−L/|a|, L], the segment II denotes the region [−L/|a| 2 , −L/|a|] and the segment III denotes the regio…

**Figure 12.6.** Figure 12.6: The dimensionless MFPT T˜(0) as a function of β = p r/DL for different values of −1 < a ≤ 0. The analytical result in Eq. (12.62) (with T˜(−L/|a|) taken as an input from numerical simulations) is in excellent agreement with numerical simulations for T˜(0). For a fi…

**Figure 12.7.** Figure 12.7: Left: The optimal value ℓ ∗ (a), at which T˜(0) achieves its minimum as a function of ℓ for a fixed a, is shown for few values of a, for −1 < a ≤ 0. Right: The optimal mean first passage time Topt(a), i.e., T˜(0) evaluated at ℓ = ℓ ∗ (a), for the same values of −1 ≤…

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

196 extracted references · 2 canonical work pages

[1]

Exact extreme, order, and sum statistics in a class of strongly correlated systems.Physical Review E, 109(1):014101, 2024

Marco Biroli, Hernán Larralde, Satya N Majumdar, and Grégory Schehr. Exact extreme, order, and sum statistics in a class of strongly correlated systems.Physical Review E, 109(1):014101, 2024

2024
[2]

Extreme statistics and spacing distribution in a brownian gas correlated by resetting.Physical Review Letters, 130(20):207101, 2023

Marco Biroli, Hernan Larralde, Satya N Majumdar, and Grégory Schehr. Extreme statistics and spacing distribution in a brownian gas correlated by resetting.Physical Review Letters, 130(20):207101, 2023

2023
[3]

Dynamically emergent correlations between particles in a switching har- monic trap.Physical Review E, 109(3):L032106, 2024

Marco Biroli, Manas Kulkarni, Satya N Majumdar, and Grégory Schehr. Dynamically emergent correlations between particles in a switching har- monic trap.Physical Review E, 109(3):L032106, 2024

2024
[4]

Majumdar, and Grégory Schehr

Marco Biroli, Satya N. Majumdar, and Grégory Schehr. Resetting dyson brownian motion.Phys. Rev. E, 112:014101, Jul 2025

2025
[5]

Critical number of walkers for diffusive search processes with resetting.Physical Review E, 107(6):064141, 2023

Marco Biroli, Satya N Majumdar, and Grégory Schehr. Critical number of walkers for diffusive search processes with resetting.Physical Review E, 107(6):064141, 2023

2023
[6]

Resetting by rescaling: Exact results for a diffusing particle in one dimension.Physical Review E, 110(4):044142, 2024

Marco Biroli, Yannick Feld, Alexander K Hartmann, Satya N Majumdar, and Grégory Schehr. Resetting by rescaling: Exact results for a diffusing particle in one dimension.Physical Review E, 110(4):044142, 2024

2024
[7]

Majumdar, Artyom Petrosyan, and Gregory Schehr

Marco Biroli, Sergio Ciliberto, Manas Kulkarni, Satya N. Majumdar, Artyom Petrosyan, and Gregory Schehr. Experimental evidence for strong emergent correlations between particles in a switching trap, 2025

2025
[8]

Cambridge University Press, 2007

Mehran Kardar.Statistical physics of particles. Cambridge University Press, 2007

2007

Show all 196 references

[9]

Elsevier, 2004

Madan Lal Mehta.Random matrices, volume 142. Elsevier, 2004

2004
[10]

Princeton university press, 2010

Peter J Forrester.Log-gases and random matrices (LMS-34). Princeton university press, 2010

2010
[11]

Introduction to ran- dom matrices theory and practice.Monograph Award, 63(54):914, 2018

Giacomo Livan, Marcel Novaes, and Pierpaolo Vivo. Introduction to ran- dom matrices theory and practice.Monograph Award, 63(54):914, 2018

2018
[12]

The central limit theorem from laplace to cauchy: changes in stochastic objectives and in analytical methods

Hans Fischer. The central limit theorem from laplace to cauchy: changes in stochastic objectives and in analytical methods. InA history of the central limit theorem: from classical to modern probability theory, pages 17–74. Springer, 2010. 189

2010
[13]

Proﬁle books, 2010

Benoit B Mandelbrot and Richard L Hudson.The (mis) behaviour of mar- kets: a fractal view of risk, ruin and reward. Proﬁle books, 2010

2010
[14]

Columbia university press, 1958

Emil Julius Gumbel.Statistics of extremes. Columbia university press, 1958

1958
[15]

Statistics of extremes in hydrology.Advances in water resources, 25(8-12):1287–1304, 2002

Richard W Katz, Marc B Parlange, and Philippe Naveau. Statistics of extremes in hydrology.Advances in water resources, 25(8-12):1287–1304, 2002

2002
[16]

Traveling waves, front selection, and exact nontrivial exponents in a random fragmentation problem

PL Krapivsky and Satya N Majumdar. Traveling waves, front selection, and exact nontrivial exponents in a random fragmentation problem. Physical review letters, 85(26):5492, 2000

2000
[17]

Extremal paths on a random cayley tree.Physical Review E, 62(6):7735, 2000

Satya N Majumdar and PL Krapivsky. Extremal paths on a random cayley tree.Physical Review E, 62(6):7735, 2000

2000
[18]

Krapivsky

Satya N Majumdar and Paul L. Krapivsky. Extreme value statistics and traveling fronts: Application to computer science.Physical Review E, 65(3):036127, 2002

2002
[19]

Extreme value statistics and trav- eling fronts: various applications.Physica A: Statistical Mechanics and its Applications, 318(1-2):161–170, 2003

Satya N Majumdar and PL Krapivsky. Extreme value statistics and trav- eling fronts: various applications.Physica A: Statistical Mechanics and its Applications, 318(1-2):161–170, 2003

2003
[20]

Understanding search trees via statistical physics.Pramana, 64:1175–1189, 2005

Satya N Majumdar, David S Dean, and Paul L Krapivsky. Understanding search trees via statistical physics.Pramana, 64:1175–1189, 2005

2005
[21]

Optimal time to sell a stock in the black–scholes model: comment on ‘thou shalt buy and hold’, by a

Satya N Majumdar and Jean-Philippe Bouchaud. Optimal time to sell a stock in the black–scholes model: comment on ‘thou shalt buy and hold’, by a. shiryaev, z. xu and xy zhou.Quantitative Finance, 8(8):753– 760, 2008

2008
[22]

Springer Science & Business Media, 2013

Paul Embrechts, Claudia Klüppelberg, and Thomas Mikosch.Modelling extremal events: for insurance and ﬁnance, volume 33. Springer Science & Business Media, 2013

2013
[23]

Applications of extreme value statistics in physics.Journal of Physics A: Mathematical and Theoretical, 48(18):183001, 2015

Jean-Yves Fortin and Maxime Clusel. Applications of extreme value statistics in physics.Journal of Physics A: Mathematical and Theoretical, 48(18):183001, 2015

2015
[24]

Random-energy model: An exactly solvable model of disordered systems.Physical Review B, 24(5):2613, 1981

Bernard Derrida. Random-energy model: An exactly solvable model of disordered systems.Physical Review B, 24(5):2613, 1981

1981
[25]

Universality classes for extreme-value statistics.Journal of Physics A: Mathematical and General, 30(23):7997, 1997

Jean-Philippe Bouchaud and Marc Mézard. Universality classes for extreme-value statistics.Journal of Physics A: Mathematical and General, 30(23):7997, 1997. 190

1997
[26]

Extreme value problems in random matrix theory and other disordered systems.Jour- nal of Statistical Mechanics: Theory and Experiment, 2007(07):P07019, 2007

Giulio Biroli, Jean-Philippe Bouchaud, and Marc Potters. Extreme value problems in random matrix theory and other disordered systems.Jour- nal of Statistical Mechanics: Theory and Experiment, 2007(07):P07019, 2007

2007
[27]

I Weissman. 2. a survey of results on extremes of independent non- identically distributed random variables.Advances in Applied Probability, 20(1):8–8, 1988

1988
[28]

Super-slowly varying functions in extreme value theory

CW Anderson. Super-slowly varying functions in extreme value theory. Journal of the Royal Statistical Society: Series B (Methodological), 40(2):197– 202, 1978

1978
[29]

Large deviations of extremes

CW Anderson. Large deviations of extremes. InStatistical Extremes and Applications, pages 325–340. Springer, 1984

1984
[30]

Tail estimates motivated by extreme value theory.The Annals of Statistics, pages 1467–1487, 1984

Richard Davis and Sidney Resnick. Tail estimates motivated by extreme value theory.The Annals of Statistics, pages 1467–1487, 1984

1984
[31]

Large deviations of tail estima- tors based on the pareto approximation.Journal of applied probability, 24(3):619–630, 1987

Richard L Smith and Ishay Weissman. Large deviations of tail estima- tors based on the pareto approximation.Journal of applied probability, 24(3):619–630, 1987

1987
[32]

Extreme value statistics of correlated random variables: a pedagogical review.Physics Reports, 840:1–32, 2020

Satya N Majumdar, Arnab Pal, and Grégory Schehr. Extreme value statistics of correlated random variables: a pedagogical review.Physics Reports, 840:1–32, 2020

2020
[33]

Maximal height scaling of kinetically growing surfaces

Subhadip Raychaudhuri, Michael Cranston, Corry Przybyla, and Yonathan Shapir. Maximal height scaling of kinetically growing surfaces. Physical review letters, 87(13):136101, 2001

2001
[34]

Statistics of extremal intensities for gaussian interfaces.Physical Review E, 68(5):056116, 2003

G Györgyi, PCW Holdsworth, B Portelli, and Z Rácz. Statistics of extremal intensities for gaussian interfaces.Physical Review E, 68(5):056116, 2003

2003
[35]

Exact maximal height distribution of ﬂuctuating interfaces.Physical review letters, 92(22):225501, 2004

Satya N Majumdar and Alain Comtet. Exact maximal height distribution of ﬂuctuating interfaces.Physical review letters, 92(22):225501, 2004

2004
[36]

Airy distribution function: from the area under a brownian excursion to the maximal height of ﬂuctuat- ing interfaces.Journal of statistical physics, 119:777–826, 2005

Satya N Majumdar and Alain Comtet. Airy distribution function: from the area under a brownian excursion to the maximal height of ﬂuctuat- ing interfaces.Journal of statistical physics, 119:777–826, 2005

2005
[37]

Level-spacing distributions and the airy kernel.Communications in Mathematical Physics, 159:151–174, 1994

Craig A Tracy and Harold Widom. Level-spacing distributions and the airy kernel.Communications in Mathematical Physics, 159:151–174, 1994

1994
[38]

On orthogonal and symplectic matrix ensembles.Communications in Mathematical Physics, 177:727–754, 1996

Craig A Tracy and Harold Widom. On orthogonal and symplectic matrix ensembles.Communications in Mathematical Physics, 177:727–754, 1996. 191

1996
[39]

Large deviations of extreme eigenvalues of random matrices.Physical review letters, 97(16):160201, 2006

David S Dean and Satya N Majumdar. Large deviations of extreme eigenvalues of random matrices.Physical review letters, 97(16):160201, 2006

2006
[40]

Extreme value statistics of eigen- values of gaussian random matrices.Physical Review E—Statistical, Non- linear, and Soft Matter Physics, 77(4):041108, 2008

David S Dean and Satya N Majumdar. Extreme value statistics of eigen- values of gaussian random matrices.Physical Review E—Statistical, Non- linear, and Soft Matter Physics, 77(4):041108, 2008

2008
[41]

Large deviations of the maximum eigenvalue for wishart and gaussian random matrices.Phys- ical review letters, 102(6):060601, 2009

Satya N Majumdar and Massimo Vergassola. Large deviations of the maximum eigenvalue for wishart and gaussian random matrices.Phys- ical review letters, 102(6):060601, 2009

2009
[42]

Top eigenvalue of a random matrix: large deviations and third order phase transition.Journal of Sta- tistical Mechanics: Theory and Experiment, 2014(1):P01012, 2014

Satya N Majumdar and Grégory Schehr. Top eigenvalue of a random matrix: large deviations and third order phase transition.Journal of Sta- tistical Mechanics: Theory and Experiment, 2014(1):P01012, 2014

2014
[43]

Solution of the generalised random energy model.Journal of Physics C: Solid State Physics, 19(13):2253, 1986

Bernard Derrida and E Gardner. Solution of the generalised random energy model.Journal of Physics C: Solid State Physics, 19(13):2253, 1986

1986
[44]

Random walk models for the spike activity of a single neuron.Biophysical journal, 4(1):41–68, 1964

George L Gerstein and Benoit Mandelbrot. Random walk models for the spike activity of a single neuron.Biophysical journal, 4(1):41–68, 1964

1964
[45]

Stochastic integrate and ﬁre models: a review on mathematical methods and their applications

Laura Sacerdote and Maria Teresa Giraudo. Stochastic integrate and ﬁre models: a review on mathematical methods and their applications. Stochastic biomathematical models: with applications to neuronal model- ing, pages 99–148, 2013

2013
[46]

Cambridge University Press, 1988

Henry Clavering Tuckwell.Introduction to theoretical neurobiology: lin- ear cable theory and dendritic structure, volume 1. Cambridge University Press, 1988

1988
[47]

World Scientiﬁc, 2014

Ralf Metzler, Sidney Redner, and Gleb Oshanin.First-passage phenom- ena and their applications, volume 35. World Scientiﬁc, 2014

2014
[48]

Elsevier, 1992

Nicolaas Godfried Van Kampen.Stochastic processes in physics and chem- istry, volume 1. Elsevier, 1992

1992
[49]

Springer Science & Business Media, 2012

William J Bell.Searching behaviour: the behavioural ecology of ﬁnding re- sources. Springer Science & Business Media, 2012

2012
[50]

Reduction of dimensionality in biological diffu- sion processes.Structural chemistry and molecular biology, 198:198–215, 1968

G Adam and M Delbrück. Reduction of dimensionality in biological diffu- sion processes.Structural chemistry and molecular biology, 198:198–215, 1968

1968
[51]

Optimal search behavior and classic foraging theory.Journal of Physics A: Mathematical and Theoretical, 42(43):434002, 2009

Frederic Bartumeus and Jordi Catalan. Optimal search behavior and classic foraging theory.Journal of Physics A: Mathematical and Theoretical, 42(43):434002, 2009. 192

2009
[52]

Cambridge University Press, 2011

Gandhimohan M Viswanathan, Marcos GE Da Luz, Ernesto P Raposo, and H Eugene Stanley.The physics of foraging: an introduction to random searches and biological encounters. Cambridge University Press, 2011

2011
[53]

Diffusion-driven mechanisms of protein translocation on nucleic acids

Otto G Berg, Robert B Winter, and Peter H Von Hippel. Diffusion-driven mechanisms of protein translocation on nucleic acids. 1. models and theory.Biochemistry, 20(24):6929–6948, 1981

1981
[54]

Kinetics of target site localization of a protein on dna: a stochastic approach.Bio- physical journal, 87(3):1640–1649, 2004

Mathieu Coppey, O Bénichou, R Voituriez, and M Moreau. Kinetics of target site localization of a protein on dna: a stochastic approach.Bio- physical journal, 87(3):1640–1649, 2004

2004
[55]

Soumendu Ghosh, Bhavya Mishra, Anatoly B Kolomeisky, and De- bashish Chowdhury. First-passage processes on a ﬁlamentous track in a dense traﬃc: optimizing diffusive search for a target in crowd- ing conditions.Journal of Statistical Mechanics: Theory and Experiment, 2018(12):1...

2018
[56]

kiss of death

Debashish Chowdhury. Laying tracks for poison delivery to “kiss of death”: Search for immune synapse by microtubules.Biophysical Jour- nal, 116(11):2057–2059, 2019

2019
[57]

Théorie de la spéculation

Louis Bachelier. Théorie de la spéculation. InAnnales scientiﬁques de l’École normale supérieure, volume 17, pages 21–86, 1900

1900
[58]

Courier Corporation, 1956

Albert Einstein.Investigations on the Theory of the Brownian Movement. Courier Corporation, 1956

1956
[59]

On the kinetic theory of brownian molecular motion and suspensions.Annals of Physics, 326(14):756–780, 1906

Marian By Smoluchowski. On the kinetic theory of brownian molecular motion and suspensions.Annals of Physics, 326(14):756–780, 1906

1906
[60]

On the statistical distribution of the widths and spac- ings of nuclear resonance levels

Eugene P Wigner. On the statistical distribution of the widths and spac- ings of nuclear resonance levels. InMathematical Proceedings of the Cam- bridge Philosophical Society, volume 47, pages 790–798. Cambridge Uni- versity Press, 1951

1951
[61]

Measurement-induced entanglement transitions in the quantum ising chain: From inﬁnite to zero clicks.Physical Review B, 103(22):224210, 2021

Xhek Turkeshi, Alberto Biella, Rosario Fazio, Marcello Dalmonte, and Marco Schiró. Measurement-induced entanglement transitions in the quantum ising chain: From inﬁnite to zero clicks.Physical Review B, 103(22):224210, 2021

2021
[62]

Stochastic re- setting and applications.Journal of Physics A: Mathematical and Theoret- ical, 53(19):193001, 2020

Martin R Evans, Satya N Majumdar, and Grégory Schehr. Stochastic re- setting and applications.Journal of Physics A: Mathematical and Theoret- ical, 53(19):193001, 2020

2020
[63]

Diffusion with stochastic reset- ting.Physical review letters, 106(16):160601, 2011

Martin R Evans and Satya N Majumdar. Diffusion with stochastic reset- ting.Physical review letters, 106(16):160601, 2011. 193

2011
[64]

Diffusion with optimal resetting

Martin R Evans and Satya N Majumdar. Diffusion with optimal resetting. Journal of Physics A: Mathematical and Theoretical, 44(43):435001, 2011

2011
[65]

Characterization of stationary states in random walks with stochastic resetting.Physical Review E, 93(2):022106, 2016

Vicenç Méndez and Daniel Campos. Characterization of stationary states in random walks with stochastic resetting.Physical Review E, 93(2):022106, 2016

2016
[66]

Non-equilibrium steady states of stochastic processes with intermittent resetting.New Journal of Physics, 18(3):033006, 2016

Stephan Eule and Jakob J Metzger. Non-equilibrium steady states of stochastic processes with intermittent resetting.New Journal of Physics, 18(3):033006, 2016

2016
[67]

Springer Science & Business Media, 2011

Malte Henkel and Michel Pleimling.Non-Equilibrium Phase Transitions: Volume 2: Ageing and Dynamical Scaling Far from Equilibrium. Springer Science & Business Media, 2011

2011
[68]

1: Absorbing Phase Transitions

Malte Henkel, Haye Hinrichsen, and Mette Lübeck.Non-equilibrium phase transitions: vol. 1: Absorbing Phase Transitions. Springer, 2008

2008
[69]

First order transition for the optimal search time of lévy ﬂights with resetting.Physical review letters, 113(22):220602, 2014

Lukasz Kusmierz, Satya N Majumdar, Sanjib Sabhapandit, and Grégory Schehr. First order transition for the optimal search time of lévy ﬂights with resetting.Physical review letters, 113(22):220602, 2014

2014
[70]

Optimal ﬁrst-arrival times in lévy ﬂights with resetting.Physical Review E, 92(5):052127, 2015

Łukasz Kuśmierz and Ewa Gudowska-Nowak. Optimal ﬁrst-arrival times in lévy ﬂights with resetting.Physical Review E, 92(5):052127, 2015

2015
[71]

Phase transitions in optimal search times: How random walkers should combine resetting and ﬂight scales

Daniel Campos and Vicenç Méndez. Phase transitions in optimal search times: How random walkers should combine resetting and ﬂight scales. Physical Review E, 92(6):062115, 2015

2015
[73]

Nist atomic spectra database (ver

Alexander Kramida, Yuri Ralchenko, Joseph Reader, et al. Nist atomic spectra database (ver. 5.3), 2015

2015
[74]

Oxford University Press, 2024

Satya N Majumdar and Gregory Schehr.Statistics of Extremes and Records in Random Sequences. Oxford University Press, 2024

2024
[75]

SIAM, 2008

Barry C Arnold, Narayanaswamy Balakrishnan, and Haikady Navada Na- garaja.A ﬁrst course in order statistics. SIAM, 2008

2008
[77]

Exact record and order statis- tics of random walks via ﬁrst-passage ideas

Grégory Schehr and Satya N Majumdar. Exact record and order statis- tics of random walks via ﬁrst-passage ideas. InFirst-passage phenomena and their applications, pages 226–251. World Scientiﬁc, 2014. 194

2014
[78]

Sur la distribution limite du terme maximum d’une serie aleatoire.Annals of mathematics, 44(3):423–453, 1943

Boris Gnedenko. Sur la distribution limite du terme maximum d’une serie aleatoire.Annals of mathematics, 44(3):423–453, 1943

1943
[79]

An introduction to probability theory and its appli- cations

William Feller et al. An introduction to probability theory and its appli- cations. 1971

1971
[80]

John Wiley & Sons, 1991

William Feller.An introduction to probability theory and its applications, Volume 2, volume 2. John Wiley & Sons, 1991

1991
[81]

Large deviations of the maximum of independent and identically distributed random variables.European Journal of Physics, 36(5):055037, 2015

Pierpaolo Vivo. Large deviations of the maximum of independent and identically distributed random variables.European Journal of Physics, 36(5):055037, 2015

2015
[82]

Large deviations in statistical physics, 2024

Hugo Touchette. Large deviations in statistical physics, 2024

2024
[83]

rightmost

Pierpaolo Vivo. Large deviations of spectral radius and “rightmost” parti- cle for random matrices/charged ﬂuids with logarithmic repulsion, 2024

2024
[84]

Stochastic resetting and large devia- tions.arXiv preprint arXiv:2412.16374, 2024

Martin R Evans and John C Sunil. Stochastic resetting and large devia- tions.arXiv preprint arXiv:2412.16374, 2024

2024 arXiv
[85]

Limit theorems for the maximum term in stationary sequences.The Annals of Mathematical Statistics, pages 502–516, 1964

Simeon M Berman. Limit theorems for the maximum term in stationary sequences.The Annals of Mathematical Statistics, pages 502–516, 1964

1964
[86]

Cambridge university press, 2001

Sidney Redner.A guide to ﬁrst-passage processes. Cambridge university press, 2001

2001
[87]

Satya N Majumdar. Universal ﬁrst-passage properties of discrete-time random walks and lévy ﬂights on a line: Statistics of the global maxi- mum and records.Physica A: Statistical Mechanics and its Applications, 389(20):4299–4316, 2010

2010
[88]

Persistence and ﬁrst-passage properties in nonequilibrium systems.Advances in Physics, 62(3):225–361, 2013

Alan J Bray, Satya N Majumdar, and Grégory Schehr. Persistence and ﬁrst-passage properties in nonequilibrium systems.Advances in Physics, 62(3):225–361, 2013

2013
[89]

A generalization of the random energy model which includes correlations between energies.Journal de Physique Lettres, 46(9):401–407, 1985

Bernard Derrida. A generalization of the random energy model which includes correlations between energies.Journal de Physique Lettres, 46(9):401–407, 1985

1985
[90]

Extreme-value statistics of hierarchi- cally correlated variables deviation from gumbel statistics and anoma- lous persistence.Physical Review E, 64(4):046121, 2001

DS Dean and Satya N Majumdar. Extreme-value statistics of hierarchi- cally correlated variables deviation from gumbel statistics and anoma- lous persistence.Physical Review E, 64(4):046121, 2001

2001
[91]

Generalized extreme value statistics and sum of correlated variables.Journal of Physics A: Mathematical and Gen- eral, 39(24):7607, 2006

Eric Bertin and Maxime Clusel. Generalized extreme value statistics and sum of correlated variables.Journal of Physics A: Mathematical and Gen- eral, 39(24):7607, 2006. 195

2006
[92]

Grégory Schehr and Satya N Majumdar. Universal asymptotic statis- tics of maximal relative height in one-dimensional solid-on-solid mod- els.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 73(5):056103, 2006

2006
[93]

Superstatistics.Physica A: Statis- tical mechanics and its applications, 322:267–275, 2003

Christian Beck and Ezechiel GD Cohen. Superstatistics.Physica A: Statis- tical mechanics and its applications, 322:267–275, 2003

2003
[94]

From time series to superstatistics.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 72(5):056133, 2005

Christian Beck, Ezechiel GD Cohen, and Harry L Swinney. From time series to superstatistics.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 72(5):056133, 2005

2005
[95]

Random matrix theory within superstatistics.Physical Re- view E—Statistical, Nonlinear, and Soft Matter Physics, 72(6):066114, 2005

AY Abul-Magd. Random matrix theory within superstatistics.Physical Re- view E—Statistical, Nonlinear, and Soft Matter Physics, 72(6):066114, 2005

2005
[96]

Disordered en- sembles of random matrices.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 77(1):011122, 2008

O Bohigas, JX de Carvalho, and Mauricio Porto Pato. Disordered en- sembles of random matrices.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 77(1):011122, 2008

2008
[97]

Superstatistical general- izations of wishart–laguerre ensembles of random matrices.Journal of Physics A: Mathematical and Theoretical, 42(17):175207, 2009

AY Abul-Magd, Gernot Akemann, and P Vivo. Superstatistical general- izations of wishart–laguerre ensembles of random matrices.Journal of Physics A: Mathematical and Theoretical, 42(17):175207, 2009

2009
[98]

Recent developments in superstatistics.Brazilian Journal of Physics, 39:357–363, 2009

Christian Beck. Recent developments in superstatistics.Brazilian Journal of Physics, 39:357–363, 2009

2009
[99]

Extreme value laws for superstatistics

Pau Rabassa and Christian Beck. Extreme value laws for superstatistics. Entropy, 16(10):5523–5536, 2014

2014
[100]

Extreme-value approach to the tsal- lis’ superstatistics.ACTA PHYSICA POLONICA SERIES B, 35(4):1375–1386, 2004

Paulina Hetman and Karina Weron. Extreme-value approach to the tsal- lis’ superstatistics.ACTA PHYSICA POLONICA SERIES B, 35(4):1375–1386, 2004

2004
[101]

Universality of market superstatistics.Physical Review E, 94(4):042305, 2016

Mateusz Denys, Tomasz Gubiec, Ryszard Kutner, Maciej Jagielski, and H Eugene Stanley. Universality of market superstatistics.Physical Review E, 94(4):042305, 2016

2016
[102]

Diffusing diffusivity: a model for anomalous, yet brownian, diffusion.Physical review letters, 113(9):098302, 2014

Mykyta V Chubynsky and Gary W Slater. Diffusing diffusivity: a model for anomalous, yet brownian, diffusion.Physical review letters, 113(9):098302, 2014

2014
[104]

The inspection paradox in stochastic resetting.Journal of Physics A: Mathematical and Theoretical, 55(2):021001, 2022

Arnab Pal, Sarah Kostinski, and Shlomi Reuveni. The inspection paradox in stochastic resetting.Journal of Physics A: Mathematical and Theoretical, 55(2):021001, 2022. 196

2022
[105]

Stochastic resetting: A (very) brief review.Frontiers in Physics, 10:789097, 2022

Shamik Gupta and Arun M Jayannavar. Stochastic resetting: A (very) brief review.Frontiers in Physics, 10:789097, 2022

2022
[106]

Experimental realization of diffusion with stochastic re- setting.The journal of physical chemistry letters, 11(17):7350–7355, 2020

Oﬁr Tal-Friedman, Arnab Pal, Amandeep Sekhon, Shlomi Reuveni, and Yael Roichman. Experimental realization of diffusion with stochastic re- setting.The journal of physical chemistry letters, 11(17):7350–7355, 2020

2020
[107]

Majumdar, and Sergio Ciliberto

Benjamin Besga, Alfred Bovon, Artyom Petrosyan, Satya N. Majumdar, and Sergio Ciliberto. Optimal mean ﬁrst-passage time for a brownian searcher subjected to resetting: Experimental and theoretical results. Phys. Rev. Res., 2:032029, Jul 2020

2020
[108]

Felix Faisant, Benjamin Besga, Artyom Petrosyan, Sergio Ciliberto, and Satya N Majumdar. Optimal mean ﬁrst-passage time of a brownian searcher with resetting in one and two dimensions: experiments, theory and numerical tests.Journal of Statistical Mechanics: Theory and Experi-...

2021
[109]

The role of sub- strate unbinding in michaelis-menten enzymatic reactions.Biophysical Journal, 106(2):677a, 2014

Shlomi Reuveni, Michael Urbakh, and Joseph Klafter. The role of sub- strate unbinding in michaelis-menten enzymatic reactions.Biophysical Journal, 106(2):677a, 2014

2014
[110]

Random walks with preferential re- locations to places visited in the past and their application to biology

Denis Boyer and Citlali Solis-Salas. Random walks with preferential re- locations to places visited in the past and their application to biology. Physical review letters, 112(24):240601, 2014

2014
[111]

Michaelis-menten re- action scheme as a uniﬁed approach towards the optimal restart prob- lem.Physical Review E, 92(6):060101, 2015

Tal Rotbart, Shlomi Reuveni, and Michael Urbakh. Michaelis-menten re- action scheme as a uniﬁed approach towards the optimal restart prob- lem.Physical Review E, 92(6):060101, 2015

2015
[112]

Majumdar, Sanjib Sabhapandit, and Grégory Schehr

Satya N. Majumdar, Sanjib Sabhapandit, and Grégory Schehr. Dynami- cal transition in the temporal relaxation of stochastic processes under resetting.Phys. Rev. E, 91:052131, May 2015

2015
[113]

Diffusion under time- dependent resetting.Journal of Physics A: Mathematical and Theoretical, 49(22):225001, 2016

Arnab Pal, Anupam Kundu, and Martin R Evans. Diffusion under time- dependent resetting.Journal of Physics A: Mathematical and Theoretical, 49(22):225001, 2016

2016
[115]

Directed random walk with ran- dom restarts: The sisyphus random walk.Physical Review E, 94(3):032132, 2016

Miquel Montero and Javier Villarroel. Directed random walk with ran- dom restarts: The sisyphus random walk.Physical Review E, 94(3):032132, 2016

2016
[116]

Diffusion with stochastic resetting at power-law times.Physical Review E, 93(6):060102, 2016

Apoorva Nagar and Shamik Gupta. Diffusion with stochastic resetting at power-law times.Physical Review E, 93(6):060102, 2016. 197

2016
[117]

First passage under restart.Physical review letters, 118(3):030603, 2017

Arnab Pal and Shlomi Reuveni. First passage under restart.Physical review letters, 118(3):030603, 2017

2017
[118]

Long time scaling behaviour for diffusion with resetting and memory.Journal of Statistical Mechanics: Theory and Experiment, 2017(2):023208, feb 2017

Denis Boyer, Martin R Evans, and Satya N Majumdar. Long time scaling behaviour for diffusion with resetting and memory.Journal of Statistical Mechanics: Theory and Experiment, 2017(2):023208, feb 2017

2017
[119]

Run and tumble particle under resetting: a renewal approach.Journal of Physics A: Mathematical and Theoretical, 51(47):475003, 2018

Martin R Evans and Satya N Majumdar. Run and tumble particle under resetting: a renewal approach.Journal of Physics A: Mathematical and Theoretical, 51(47):475003, 2018

2018
[120]

Random search with resetting: a uniﬁed renewal approach.Physical review letters, 121(5):050601, 2018

Aleksei Chechkin and Igor M Sokolov. Random search with resetting: a uniﬁed renewal approach.Physical review letters, 121(5):050601, 2018

2018
[121]

Lotka–volterra systems with stochastic resetting.Journal of Physics A: Mathematical and Theo- retical, 51(40):405601, 2018

Gabriel Mercado-Vásquez and Denis Boyer. Lotka–volterra systems with stochastic resetting.Journal of Physics A: Mathematical and Theo- retical, 51(40):405601, 2018

2018
[122]

Time-dependent den- sity of diffusion with stochastic resetting is invariant to return speed

Arnab Pal, Łukasz Kuśmierz, and Shlomi Reuveni. Time-dependent den- sity of diffusion with stochastic resetting is invariant to return speed. Physical Review E, 100(4):040101, 2019

2019
[123]

Transport properties and ﬁrst-arrival statistics of random motion with stochastic reset times.Physical Review E, 99(1):012141, 2019

Axel Masó-Puigdellosas, Daniel Campos, and Vicenç Méndez. Transport properties and ﬁrst-arrival statistics of random motion with stochastic reset times.Physical Review E, 99(1):012141, 2019

2019
[124]

Search with home returns provides advantage under high uncertainty.Physical Review Re- search, 2(4):043174, 2020

Arnab Pal, Łukasz Kuśmierz, and Shlomi Reuveni. Search with home returns provides advantage under high uncertainty.Physical Review Re- search, 2(4):043174, 2020

2020
[125]

Resetting processes with nonin- stantaneous return.Physical Review E, 101(5):052130, 2020

Anna S Bodrova and Igor M Sokolov. Resetting processes with nonin- stantaneous return.Physical Review E, 101(5):052130, 2020

2020
[126]

Brownian motion under noninstan- taneous resetting in higher dimensions.Physical Review E, 102(3):032129, 2020

Anna S Bodrova and Igor M Sokolov. Brownian motion under noninstan- taneous resetting in higher dimensions.Physical Review E, 102(3):032129, 2020

2020
[127]

Optimization in ﬁrst- passage resetting.Physical Review Letters, 125(5):050602, 2020

B De Bruyne, Julien Randon-Furling, and S Redner. Optimization in ﬁrst- passage resetting.Physical Review Letters, 125(5):050602, 2020

2020
[128]

Diffusive search for a stochastically-gated target with resetting.Journal of Physics A: Mathematical and Theoretical, 53(42):425001, 2020

Paul C Bressloff. Diffusive search for a stochastically-gated target with resetting.Journal of Physics A: Mathematical and Theoretical, 53(42):425001, 2020

2020
[129]

Diffusive search with spatially dependent resetting

Ross G Pinsky. Diffusive search with spatially dependent resetting. Stochastic Processes and their Applications, 130(5):2954–2973, 2020. 198

2020
[130]

Optimal resetting brownian bridges via enhanced ﬂuctuations.Physical Review Letters, 128(20):200603, 2022

Benjamin De Bruyne, Satya N Majumdar, and Grégory Schehr. Optimal resetting brownian bridges via enhanced ﬂuctuations.Physical Review Letters, 128(20):200603, 2022

2022
[131]

Time to reach the maximum for a stationary stochastic process.Physical Review E, 106(5):054110, 2022

Francesco Mori, Satya N Majumdar, and Grégory Schehr. Time to reach the maximum for a stationary stochastic process.Physical Review E, 106(5):054110, 2022

2022
[132]

Effect of stochastic re- setting on brownian motion with stochastic diffusion coeﬃcient.Journal of Physics A: Mathematical and Theoretical, 55(41):414002, 2022

Ion Santra, Urna Basu, and Sanjib Sabhapandit. Effect of stochastic re- setting on brownian motion with stochastic diffusion coeﬃcient.Journal of Physics A: Mathematical and Theoretical, 55(41):414002, 2022

2022
[133]

Resetting in stochastic opti- mal control.Physical Review Research, 5(1):013122, 2023

Benjamin De Bruyne and Francesco Mori. Resetting in stochastic opti- mal control.Physical Review Research, 5(1):013122, 2023

2023
[134]

Entropy production of resetting processes.Physical Review Research, 5(2):023103, 2023

Francesco Mori, Kristian Stølevik Olsen, and Supriya Krishnamurthy. Entropy production of resetting processes.Physical Review Research, 5(2):023103, 2023

2023
[135]

Stochastic resetting prevails over sharp restart for broad target distributions.arXiv preprint arXiv:2410.01941, 2024

Martin R Evans and Somrita Ray. Stochastic resetting prevails over sharp restart for broad target distributions.arXiv preprint arXiv:2410.01941, 2024

2024 arXiv
[136]

Exact statistical mechanics of a one-dimensional sys- tem with coulomb forces.Journal of Mathematical Physics, 2(5):682–693, 1961

Andrew Lenard. Exact statistical mechanics of a one-dimensional sys- tem with coulomb forces.Journal of Mathematical Physics, 2(5):682–693, 1961

1961
[137]

The one-dimensional plasma.Advances in chemical physics, 4:201–224, 1962

Stephen Prager. The one-dimensional plasma.Advances in chemical physics, 4:201–224, 1962

1962
[138]

Statistical mechanics of a one-dimensional coulomb system with a uniform charge background

Rodney James Baxter. Statistical mechanics of a one-dimensional coulomb system with a uniform charge background. InMathemati- cal Proceedings of the Cambridge Philosophical Society, volume 59, pages 779–787. Cambridge University Press, 1963

1963
[139]

Exact extremal statistics in the classical 1d coulomb gas.Physical review letters, 119(6):060601, 2017

Abhishek Dhar, Anupam Kundu, Satya N Majumdar, Sanjib Sabhapan- dit, and Grégory Schehr. Exact extremal statistics in the classical 1d coulomb gas.Physical review letters, 119(6):060601, 2017

2017
[140]

Fluctuations and ﬁrst- passage properties of systems of brownian particles with reset.Physical Review E, 106(2):024117, 2022

Ohad Vilk, Michael Assaf, and Baruch Meerson. Fluctuations and ﬁrst- passage properties of systems of brownian particles with reset.Physical Review E, 106(2):024117, 2022

2022
[141]

Academic press, 2014

Izrail Solomonovich Gradshteyn and Iosif Moiseevich Ryzhik.Table of integrals, series, and products. Academic press, 2014. 199

2014
[142]

Anomalous diffusion in disordered media: statistical mechanisms, models and physical appli- cations.Physics reports, 195(4-5):127–293, 1990

Jean-Philippe Bouchaud and Antoine Georges. Anomalous diffusion in disordered media: statistical mechanisms, models and physical appli- cations.Physics reports, 195(4-5):127–293, 1990

1990
[143]

Mode-coupling theory for the pasty rheology of soft glassy materials.Physical review letters, 81(14):2934, 1998

Pascal Hébraud and François Lequeux. Mode-coupling theory for the pasty rheology of soft glassy materials.Physical review letters, 81(14):2934, 1998

1998
[144]

Quantum dynamics with stochastic reset.Physical Review B, 98(10):104309, 2018

B Mukherjee, K Sengupta, and Satya N Majumdar. Quantum dynamics with stochastic reset.Physical Review B, 98(10):104309, 2018

2018
[145]

Designing nonequilibrium states of quantum matter through stochastic resetting.Physical Review B, 104(18):L180302, 2021

Gabriele Perfetto, Federico Carollo, Matteo Magoni, and Igor Lesanovsky. Designing nonequilibrium states of quantum matter through stochastic resetting.Physical Review B, 104(18):L180302, 2021

2021
[146]

Dynamics of closed quantum systems under stochastic resetting.Journal of Physics A: Math- ematical and Theoretical, 56(3):034001, 2023

Francisco J Sevilla and Andrea Valdés-Hernández. Dynamics of closed quantum systems under stochastic resetting.Journal of Physics A: Math- ematical and Theoretical, 56(3):034001, 2023

2023
[147]

Generating entanglement by quantum resetting.Physical Review A, 108(6):062210, 2023

Manas Kulkarni and Satya N Majumdar. Generating entanglement by quantum resetting.Physical Review A, 108(6):062210, 2023

2023
[148]

Engineered swift equilibration of a brown- ian particle.Nature physics, 12(9):843–846, 2016

Ignacio A Martínez, Artyom Petrosyan, David Guéry-Odelin, Emmanuel Trizac, and Sergio Ciliberto. Engineered swift equilibration of a brown- ian particle.Nature physics, 12(9):843–846, 2016

2016
[149]

Work ﬂuctuations and jarzynski equality in stochastic resetting.Physical review letters, 124(11):110608, 2020

Deepak Gupta, Carlos A Plata, and Arnab Pal. Work ﬂuctuations and jarzynski equality in stochastic resetting.Physical review letters, 124(11):110608, 2020

2020
[150]

Shortcuts to adiabaticity: Concepts, methods, and applications.Reviews of Modern Physics, 91(4):045001, 2019

David Guéry-Odelin, Andreas Ruschhaupt, Anthony Kiely, Erik Tor- rontegui, Soﬁa Martínez-Garaot, and Juan Gonzalo Muga. Shortcuts to adiabaticity: Concepts, methods, and applications.Reviews of Modern Physics, 91(4):045001, 2019

2019
[151]

Optimal work in a harmonic trap with bounded stiffness.Physical Review E, 99(1):012140, 2019

Carlos A Plata, David Guéry-Odelin, E Trizac, and A Prados. Optimal work in a harmonic trap with bounded stiffness.Physical Review E, 99(1):012140, 2019

2019
[152]

Thermal bath engineer- ing for swift equilibration.Physical Review E, 98(1):010104, 2018

Marie Chupeau, Benjamin Besga, David Guéry-Odelin, Emmanuel Trizac, Artyom Petrosyan, and Sergio Ciliberto. Thermal bath engineer- ing for swift equilibration.Physical Review E, 98(1):010104, 2018

2018
[153]

Intermittent resetting potentials.Journal of Statistical Me- chanics: Theory and Experiment, 2020(11):113203, 2020

Gabriel Mercado-Vásquez, Denis Boyer, Satya N Majumdar, and Gré- gory Schehr. Intermittent resetting potentials.Journal of Statistical Me- chanics: Theory and Experiment, 2020(11):113203, 2020. 200

2020
[154]

Stochas- tic resetting with stochastic returns using external trap.Journal of Physics A: Mathematical and Theoretical, 54(2):025003, 2020

Deepak Gupta, Carlos A Plata, Anupam Kundu, and Arnab Pal. Stochas- tic resetting with stochastic returns using external trap.Journal of Physics A: Mathematical and Theoretical, 54(2):025003, 2020

2020
[155]

Brownian motion under intermittent harmonic potentials.Journal of Physics A: Mathematical and Theoretical, 54(33):334001, 2021

Ion Santra, Santanu Das, and Sujit Kumar Nath. Brownian motion under intermittent harmonic potentials.Journal of Physics A: Mathematical and Theoretical, 54(33):334001, 2021

2021
[156]

Stochastic har- monic trapping of a lévy walk: transport and ﬁrst-passage dynamics un- der soft resetting strategies.New Journal of Physics, 24(3):033003, 2022

Pengbo Xu, Tian Zhou, Ralf Metzler, and Weihua Deng. Stochastic har- monic trapping of a lévy walk: transport and ﬁrst-passage dynamics un- der soft resetting strategies.New Journal of Physics, 24(3):033003, 2022

2022
[157]

Work ﬂuctuations for diffusion dynamics submitted to stochastic return.New Journal of Physics, 24(11):113034, 2022

Deepak Gupta and Carlos A Plata. Work ﬂuctuations for diffusion dynamics submitted to stochastic return.New Journal of Physics, 24(11):113034, 2022

2022
[158]

Non-equilibrium thermodynamics of diffusion in ﬂuctuating potentials.Journal of Physics A: Mathematical and Theoretical, 55(27):274004, 2022

Henry Alston, Luca Cocconi, and Thibault Bertrand. Non-equilibrium thermodynamics of diffusion in ﬂuctuating potentials.Journal of Physics A: Mathematical and Theoretical, 55(27):274004, 2022

2022
[159]

Gabriel Mercado-Vásquez, Denis Boyer, and Satya N Majumdar. Reduc- ing mean ﬁrst passage times with intermittent conﬁning potentials: a realization of resetting processes.Journal of Statistical Mechanics: The- ory and Experiment, 2022(9):093202, 2022

2022
[160]

On the theory of the brow- nian motion.Physical review, 36(5):823, 1930

George E Uhlenbeck and Leonard S Ornstein. On the theory of the brow- nian motion.Physical review, 36(5):823, 1930

1930
[161]

Cambridge university press, 2010

Frank WJ Olver.NIST handbook of mathematical functions hardback and CD-ROM. Cambridge university press, 2010

2010
[162]

Random difference equations and renewal theory for products of random matrices

Harry Kesten. Random difference equations and renewal theory for products of random matrices. 1973

1973
[163]

A limit law for random walk in a random environment.Compositio mathematica, 30(2):145–168, 1975

Harry Kesten, Mykyta V Kozlov, and Frank Spitzer. A limit law for random walk in a random environment.Compositio mathematica, 30(2):145–168, 1975

1975
[164]

Singular behaviour of certain inﬁnite products of random 2×2 matrices.Journal of Physics A: Mathe- matical and General, 16(12):2641, 1983

Bernard Derrida and HJ715727 Hilhorst. Singular behaviour of certain inﬁnite products of random 2×2 matrices.Journal of Physics A: Mathe- matical and General, 16(12):2641, 1983

1983
[165]

Convergence in distribution of prod- ucts of random matrices.Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 67:363–386, 1984

Harry Kesten and Frank Spitzer. Convergence in distribution of prod- ucts of random matrices.Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 67:363–386, 1984. 201

1984
[166]

On the distribution of a random variable occurring in 1d disor- dered systems.Journal of Physics A: Mathematical and General, 18(3):501, 1985

Claude de Calan, Jean-Marc Luck, Theo M Nieuwenhuizen, and Dimitri Petritis. On the distribution of a random variable occurring in 1d disor- dered systems.Journal of Physics A: Mathematical and General, 18(3):501, 1985

1985
[167]

Implicit renewal theory and tails of solutions of ran- dom equations.The Annals of Applied Probability, pages 126–166, 1991

Charles M Goldie. Implicit renewal theory and tails of solutions of ran- dom equations.The Annals of Applied Probability, pages 126–166, 1991

1991
[168]

Large deviations for solutions to stochastic recurrence equations under kesten’s condi- tion

D Buraczewski, E Damek, T Mikosch, and J Zienkiewicz. Large deviations for solutions to stochastic recurrence equations under kesten’s condi- tion. 2013

2013
[169]

Ma- trix kesten recursion, inverse-wishart ensemble and fermions in a morse potential.Journal of Physics A: Mathematical and Theoretical, 54(25):255201, 2021

Tristan Gautié, Jean-Philippe Bouchaud, and Pierre Le Doussal. Ma- trix kesten recursion, inverse-wishart ensemble and fermions in a morse potential.Journal of Physics A: Mathematical and Theoretical, 54(25):255201, 2021

2021
[170]

Active par- ticle in a harmonic trap driven by a resetting noise: an approach via kesten variables.Journal of Physics A: Mathematical and Theoretical, 56(47):475002, 2023

Mathis Guéneau, Satya N Majumdar, and Grégory Schehr. Active par- ticle in a harmonic trap driven by a resetting noise: an approach via kesten variables.Journal of Physics A: Mathematical and Theoretical, 56(47):475002, 2023

2023
[171]

The generalised product moment distribution in samples from a normal multivariate population.Biometrika, 20(1/2):32–52, 1928

John Wishart. The generalised product moment distribution in samples from a normal multivariate population.Biometrika, 20(1/2):32–52, 1928

1928
[172]

Cambridge University Press, 2020

Marc Potters and Jean-Philippe Bouchaud.A ﬁrst course in random matrix theory: for physicists, engineers and data scientists. Cambridge University Press, 2020

2020
[173]

John Wiley & Sons, 2004

Herbert A David and Haikady N Nagaraja.Order statistics. John Wiley & Sons, 2004

2004
[174]

A brownian-motion model for the eigenvalues of a random matrix.Journal of Mathematical Physics, 3(6):1191–1198, 1962

Freeman J Dyson. A brownian-motion model for the eigenvalues of a random matrix.Journal of Mathematical Physics, 3(6):1191–1198, 1962

1962
[175]

Statistical theory of the energy levels of complex sys- tems

Freeman J Dyson. Statistical theory of the energy levels of complex sys- tems. i.Journal of Mathematical Physics, 3(1):140–156, 1962

1962
[176]

Non-intersecting brownian bridges in the ﬂat-to-ﬂat geometry.Journal of Statistical Physics, 183(3):49, 2021

Jacek Grela, Satya N Majumdar, and Grégory Schehr. Non-intersecting brownian bridges in the ﬂat-to-ﬂat geometry.Journal of Statistical Physics, 183(3):49, 2021

2021
[177]

Distribution of the time at which n vicious walkers reach their maximal height.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 83(6):061146, 2011

Joachim Rambeau and Grégory Schehr. Distribution of the time at which n vicious walkers reach their maximal height.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 83(6):061146, 2011

2011
[178]

Matrix models for beta ensembles

Ioana Dumitriu and Alan Edelman. Matrix models for beta ensembles. Journal of Mathematical Physics, 43(11):5830–5847, 11 2002. 202

2002
[179]

Statistical theory of the energy levels of complex systems

Freeman J Dyson and Madan Lal Mehta. Statistical theory of the energy levels of complex systems. iv.Journal of Mathematical Physics, 4(5):701– 712, 1963

1963
[180]

Gaussian ﬂuctuation in random ma- trices.Physical Review Letters, 75(1):69, 1995

Ovidiu Costin and Joel L Lebowitz. Gaussian ﬂuctuation in random ma- trices.Physical Review Letters, 75(1):69, 1995

1995
[181]

M. M. Fogler and B. I. Shklovskii. Probability of an eigenvalue number ﬂuctuation in an interval of a random matrix spectrum.Phys. Rev. Lett., 74:3312–3315, Apr 1995

1995
[182]

Phase transitions and edge scaling of number variance in gaussian ran- dom matrices.Physical review letters, 112(25):254101, 2014

Ricardo Marino, Satya N Majumdar, Grégory Schehr, and Pierpaolo Vivo. Phase transitions and edge scaling of number variance in gaussian ran- dom matrices.Physical review letters, 112(25):254101, 2014

2014
[183]

Random matrices and entanglement entropy of trapped fermi gases.Physical Review A, 91(1):012303, 2015

Pasquale Calabrese, Pierre Le Doussal, and Satya N Majumdar. Random matrices and entanglement entropy of trapped fermi gases.Physical Review A, 91(1):012303, 2015

2015
[184]

Number statistics forβ-ensembles of random matrices: applications to trapped fermions at zero temperature.Physical Review E, 94(3):032115, 2016

Ricardo Marino, Satya N Majumdar, Grégory Schehr, and Pierpaolo Vivo. Number statistics forβ-ensembles of random matrices: applications to trapped fermions at zero temperature.Physical Review E, 94(3):032115, 2016

2016
[185]

Hyperuniform states of matter.Physics Reports, 745:1–95, 2018

Salvatore Torquato. Hyperuniform states of matter.Physics Reports, 745:1–95, 2018

2018
[186]

Optimal resetting strategies for search pro- cesses in heterogeneous environments.New Journal of Physics, 25(11):113031, 2023

Gregorio García-Valladares, Carlos A Plata, Antonio Prados, and Alessandro Manacorda. Optimal resetting strategies for search pro- cesses in heterogeneous environments.New Journal of Physics, 25(11):113031, 2023

2023
[187]

Optimal stochastic restart renders ﬂuctuations in ﬁrst passage times universal.Physical review letters, 116(17):170601, 2016

Shlomi Reuveni. Optimal stochastic restart renders ﬂuctuations in ﬁrst passage times universal.Physical review letters, 116(17):170601, 2016

2016
[188]

Diffusion with partial resetting.Phys

Oﬁr Tal-Friedman, Yael Roichman, and Shlomi Reuveni. Diffusion with partial resetting.Phys. Rev. E, 106:054116, Nov 2022

2022
[189]

An advection-diffusion process with proportional reset- ting.arXiv preprint arXiv:2204.07215, 2022

J Kevin Pierce. An advection-diffusion process with proportional reset- ting.arXiv preprint arXiv:2204.07215, 2022

2022 arXiv
[190]

Time-dependent probability den- sity function for partial resetting dynamics.New Journal of Physics, 25(8):082002, 2023

Costantino Di Bello, Aleksei V Chechkin, Alexander K Hartmann, Zbig- niew Palmowski, and Ralf Metzler. Time-dependent probability den- sity function for partial resetting dynamics.New Journal of Physics, 25(8):082002, 2023. 203

2023
[191]

Thermodynamic work of partial resetting.Journal of Physics A: Mathematical and Theoretical, 57(24):245001, 2024

Kristian Stølevik Olsen and Deepak Gupta. Thermodynamic work of partial resetting.Journal of Physics A: Mathematical and Theoretical, 57(24):245001, 2024

2024
[192]

Stochastic walker with variable long jumps.Physical Review E, 108(1):014135, 2023

Upendra Harbola. Stochastic walker with variable long jumps.Physical Review E, 108(1):014135, 2023

2023
[193]

A functional differential equation arising in modelling of cell growth.The ANZIAM Journal, 30(4):424–435, 1989

Alistair J Hall and GC Wake. A functional differential equation arising in modelling of cell growth.The ANZIAM Journal, 30(4):424–435, 1989

1989
[194]

A ﬁrst passage time distribution for a discrete version of the ornstein–uhlenbeck process.Journal of Physics A: Mathematical and General, 37(12):3759, 2004

Hernan Larralde. A ﬁrst passage time distribution for a discrete version of the ornstein–uhlenbeck process.Journal of Physics A: Mathematical and General, 37(12):3759, 2004

2004
[195]

Inelastic collapse of a ball bouncing on a randomly vibrating platform.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 76(3):031130, 2007

Satya N Majumdar and Michael J Kearney. Inelastic collapse of a ball bouncing on a randomly vibrating platform.Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, 76(3):031130, 2007

2007
[196]

Brow- nian yet non-gaussian diffusion: from superstatistics to subordination of diffusing diffusivities.Physical Review X, 7(2):021002, 2017

Aleksei V Chechkin, Flavio Seno, Ralf Metzler, and Igor M Sokolov. Brow- nian yet non-gaussian diffusion: from superstatistics to subordination of diffusing diffusivities.Physical Review X, 7(2):021002, 2017

2017
[197]

A model of non-gaussian dif- fusion in heterogeneous media.Journal of Physics A: Mathematical and Theoretical, 51(14):145602, 2018

Yann Lanoiselée and Denis S Grebenkov. A model of non-gaussian dif- fusion in heterogeneous media.Journal of Physics A: Mathematical and Theoretical, 51(14):145602, 2018

2018
[198]

Packets of diffusing particles exhibit uni- versal exponential tails.Physical review letters, 124(6):060603, 2020

Eli Barkai and Stanislav Burov. Packets of diffusing particles exhibit uni- versal exponential tails.Physical review letters, 124(6):060603, 2020

2020
[199]

Anomalous yet brownian.Proceedings of the National Academy of Sci- ences, 106(36):15160–15164, 2009

Bo Wang, Stephen M Anthony, Sung Chul Bae, and Steve Granick. Anomalous yet brownian.Proceedings of the National Academy of Sci- ences, 106(36):15160–15164, 2009

2009
[200]

Heterogeneities shape passive intracel- lular transport.Biophysical journal, 117(2):203–213, 2019

Patrick Witzel, Maria Götz, Yann Lanoiselée, Thomas Franosch, Denis S Grebenkov, and Doris Heinrich. Heterogeneities shape passive intracel- lular transport.Biophysical journal, 117(2):203–213, 2019. 204

2019

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Exact extreme, order, and sum statistics in a class of strongly correlated systems.Physical Review E, 109(1):014101, 2024

Marco Biroli, Hernán Larralde, Satya N Majumdar, and Grégory Schehr. Exact extreme, order, and sum statistics in a class of strongly correlated systems.Physical Review E, 109(1):014101, 2024

2024

[2] [2]

Extreme statistics and spacing distribution in a brownian gas correlated by resetting.Physical Review Letters, 130(20):207101, 2023

Marco Biroli, Hernan Larralde, Satya N Majumdar, and Grégory Schehr. Extreme statistics and spacing distribution in a brownian gas correlated by resetting.Physical Review Letters, 130(20):207101, 2023

2023

[3] [3]

Dynamically emergent correlations between particles in a switching har- monic trap.Physical Review E, 109(3):L032106, 2024

Marco Biroli, Manas Kulkarni, Satya N Majumdar, and Grégory Schehr. Dynamically emergent correlations between particles in a switching har- monic trap.Physical Review E, 109(3):L032106, 2024

2024

[4] [4]

Majumdar, and Grégory Schehr

Marco Biroli, Satya N. Majumdar, and Grégory Schehr. Resetting dyson brownian motion.Phys. Rev. E, 112:014101, Jul 2025

2025

[5] [5]

Critical number of walkers for diffusive search processes with resetting.Physical Review E, 107(6):064141, 2023

Marco Biroli, Satya N Majumdar, and Grégory Schehr. Critical number of walkers for diffusive search processes with resetting.Physical Review E, 107(6):064141, 2023

2023

[6] [6]

Resetting by rescaling: Exact results for a diffusing particle in one dimension.Physical Review E, 110(4):044142, 2024

Marco Biroli, Yannick Feld, Alexander K Hartmann, Satya N Majumdar, and Grégory Schehr. Resetting by rescaling: Exact results for a diffusing particle in one dimension.Physical Review E, 110(4):044142, 2024

2024

[7] [7]

Majumdar, Artyom Petrosyan, and Gregory Schehr

Marco Biroli, Sergio Ciliberto, Manas Kulkarni, Satya N. Majumdar, Artyom Petrosyan, and Gregory Schehr. Experimental evidence for strong emergent correlations between particles in a switching trap, 2025

2025

[8] [8]

Cambridge University Press, 2007

Mehran Kardar.Statistical physics of particles. Cambridge University Press, 2007

2007