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This survey uses scaling-limit theorems to turn the question of how fast BPS and Zig-Zag samplers mix into concrete complexity numbers: O(d²) versus O(d) per sample on Gaussian targets, and O(ε⁻¹) versus O(ε⁻²) events on ridges.

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2026-08-01 04:40 UTC pith:T6ORP6VL

load-bearing objection Useful survey of PDMC scaling results, but the anisotropy complexity claims don't match the survey's own rate formula and should be checked against the source theorem. the 2 major comments →

arxiv 2607.22449 v1 pith:T6ORP6VL submitted 2026-07-24 stat.CO math.PR

Scaling Results for Piecewise Deterministic Monte Carlo : A Survey

Joris Bierkens This is my paper
classification stat.CO math.PR MSC 60J2565C0562F15
keywords piecewise deterministic Monte CarloBouncy Particle SamplerZig-Zag processscaling limitshigh-dimensional scalinganisotropic targetssubsamplingcontrol variates
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This survey collects quantitative scaling-limit results for two continuous-time samplers, the Bouncy Particle Sampler and the Zig-Zag process. Its central message is that the two algorithms have complementary strengths: on isotropic high-dimensional Gaussians the Zig-Zag process costs O(d) per independent sample while the Bouncy Particle Sampler costs O(d²); on narrow ridge targets the ranking flips, with BPS needing only O(ε⁻¹) switching events compared with Zig-Zag's O(ε⁻²). The survey also covers a functional central limit theorem, exponential ergodicity conditions, and a big-data analysis showing that a control-variate subsampled Zig-Zag process reproduces the canonical sampler's convergence at O(1) per-event cost rather than O(n). A sympathetic reader should take away that PDMC samplers now come with precise dimension, anisotropy, and dataset-size complexity statements, not just heuristic speed comparisons.

Core claim

The paper's own claims, stated as results: for d-dimensional standard Gaussians, the BPS first-coordinate process converges after time acceleration by d to an Ornstein-Uhlenbeck process and its log-density process likewise accelerates by d, giving O(d²) operations per nearly independent sample; the ZZP's coordinates already move at unit speed, giving O(d) (or O(d²) without a coordinate-exploiting implementation). For anisotropic Gaussian targets with ridge width ε, the BPS reaches its limit without time rescaling and costs O(ε⁻¹) events, while the ZZP needs acceleration ε⁻¹ and costs O(ε⁻²) events, with an explicit angle-dependent speed except at special angles. In the big-data regime, the Z

What carries the argument

The unifying mechanism is scaling-limit analysis: instead of tracking an exact finite-dimensional sampler, the theorems pass to a limit (d→∞, ε↓0, n→∞) and identify the rescaled process with a tractable limit—Ornstein-Uhlenbeck diffusions for coordinates and log-density, an ODE with jumps for ridge BPS, or fluid-limit ODEs for transient big-data ZZP. The load-bearing device in the ridge analysis is a two-timescale averaging reduction: the fast ridge coordinate is asserted to settle to its stationary distribution before the slow coordinate moves, reducing the fast dynamics to an averaged drift and allowing an OU/ODE limit for the slow coordinate. In the big-data analysis, Poisson thinning wit

Load-bearing premise

The ridge-scaling results rely on the assumption that the fast ridge coordinate reaches stationarity before the slow coordinate changes, so the slow dynamics can be averaged over that fast equilibrium; if this separation fails, the stated Ornstein-Uhlenbeck and ODE limits need correction.

What would settle it

Simulate the Zig-Zag process on rotated Gaussian ridges U(x) = ½ xᵀ R(−θ) Λ⁻¹_ε R(θ) x for ε from 10⁻² down to 10⁻⁶ and several θ, recording the autocorrelation time of the slow coordinate; if ε² times the number of switching events to decorrelate does not converge to a finite, angle-dependent constant, the OU limit of the ridge theorem, and the averaging reduction behind it, is falsified.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • On high-dimensional Gaussian targets, an optimized Zig-Zag implementation needs O(d) computations per approximately independent sample, versus O(d²) for BPS; plain implementations erase Zig-Zag's advantage.
  • On ε-narrow ridge targets, BPS requires O(ε⁻¹) switching events per independent sample versus O(ε⁻²) for Zig-Zag, matching the random-walk Metropolis complexity; so BPS, not ZZP, is the PDMC choice for strongly anisotropic posteriors.
  • For Zig-Zag with control-variate subsampling in the big-data regime, the stationary scaling is the same as the canonical full-data Zig-Zag, with per-event cost O(1) instead of O(n): a factor-O(n) speedup at no loss of mixing.
  • The refreshment rate of BPS has a scale-invariant tuning criterion: the expected fraction of refreshment jumps that maximizes speed is 0.7812 (at the numerically optimal refreshment rate for Gaussian targets).
  • A functional central limit theorem holds under exponential ergodicity conditions, so ergodic averages of these samplers are asymptotically normal, and the asymptotic variance is accessible through the Poisson equation (explicitly for one-dimensional Zig-Zag).

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the two-timescale separation is not universal, the ridge ranking may be a Gaussian artifact; a natural extension is to test the O(ε⁻¹) versus O(ε⁻²) event counts on non-Gaussian ridge targets (e.g., curved or heavy-tailed ridges), where the fast coordinate may not equilibrate before the slow coordinate moves.
  • The high-dimensional Zig-Zag O(d) result is implementation-coupled; for correlated targets with naive coordinate-wise implementation, the per-sample cost may scale with the number of active coordinates, suggesting that preconditioned or adaptive versions deserve their own scaling analysis.
  • The control-variate result suggests a broader recipe: any unbiased gradient estimator whose variance vanishes near the mode inherits the canonical sampler's convergence; this could be tested with batched or sketch-based gradient estimators beyond single-datum subsampling.
  • The 0.7812 refreshment-fraction rule, derived for Gaussians, is plausibly a robust BPS tuning heuristic for other targets, since it is expressed in scale-invariant event fractions rather than in absolute rates; verifying this on multimodal targets would be a cheap experiment.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This survey reviews scaling results for two piecewise deterministic Monte Carlo samplers: the Bouncy Particle Sampler (BPS) and the Zig-Zag Process (ZZP). It collects results on ergodicity, functional CLTs, high-dimensional Gaussian scaling limits, scaling under anisotropic/ridged targets, and scaling in the big-data regime with subsampling. The paper reports quantitative complexity comparisons: in high dimension, BPS needs O(d) time speed-up and O(d) operations per event, while ZZP needs O(d) events per unit time but O(1) cost per event; for ε-ridged targets it claims BPS needs O(ε^{-1}) switching events per independent sample and ZZP O(ε^{-2}); and in the big-data setting, control-variate subsampling gives the same convergence rate as the canonical sampler at O(1) per-event cost instead of O(n). The theorems are stated without proofs, with references to the author's prior work.

Significance. If the reported scaling results are correct, the survey provides a valuable synthesis of quantitative efficiency results for two important PDMC algorithms. Its strengths include a clear organizational structure, honest disclosure of an unresolved exceptional case (θ=kπ/4 with odd k in Section 6), and explicit complexity tables that make the comparisons concrete. The big-data control-variate result, if accurate, is significant for Bayesian computation. However, the Section 6 complexity conclusions are not supported by the survey's own equations as written, and the central anisotropic scaling claim must be reconciled with the displayed switching-rate formula. Because the survey's main contribution is precisely these scaling conclusions, this issue is load-bearing.

major comments (2)
  1. [Section 6, Eq. (1) and paragraph after Theorem 6.1] The statement that "the number of switching events per unit time of both processes scales as ε^{-1}" is inconsistent with Eq. (1). For U_{θ,ε}, write Y=Λ_ε^{-1/2}R_θ X; under π, Y∼N(0,I). Then ∇_xU = R(-θ)Λ_ε^{-1/2}Y. Hence E[λ_i] = 1/2 E|(R(-θ)Λ_ε^{-1/2}Y)_i| = O(ε^{-1/2}) for generic θ, and the BPS bounce rate E[(⟨v,∇U⟩)_+] is also O(ε^{-1/2}). Consequently the conclusions that "BPS requires O(ε^{-1}) switching events" and "ZZP requires O(ε^{-2}) switching events" are unsupported as stated. The ε^{-1} time rescaling in Theorem 6.1(ii) also does not follow from a velocity-flip process with flip rate O(ε^{-1/2}); the natural diffusive time scale would be O(ε^{-1/2}). Please reconcile with [14] or correct the statements.
  2. [Section 6, paragraph before Theorem 6.1] The limit theorem rests on the assertion that the fast coordinate y² "quickly converges to its stationary distribution" before the slow coordinate moves. No hypotheses or proof sketch for this adiabatic/averaging step are given; the survey defers to [14]. Since this two-timescale separation is load-bearing for the OU limit (at speed Ω_θ) and for the BPS ODE-with-jumps limit, the survey should state the precise condition from [14] or explicitly mark the reduction as heuristic. The disclosed exceptional angles θ=kπ/4 (odd k) show that the separation is not uniform, so more care is needed.
minor comments (5)
  1. [Table 3] "ZZO" appears to be a typo for "ZZ" or "ZZP".
  2. [Section 5, Figure 1] The values λ_r=1.424 and the refreshment-jump ratio 0.7812 are quoted without the promised "semi-analytical expression." Please include the expression or a precise pointer to [13]. The further claim that the ratio is a "suitable criterion" for general tuning needs justification or qualification.
  3. [Section 6, Figure 2] The figure lacks axis labels and units, and the "explicit (but complicated)" expression for Ω_θ is not given. Either include the formula or provide a precise reference to [14].
  4. [Section 7, first paragraph] There is a typographical backslash in "\nabla U(x)"; it should read "\nabla U(x)" without the stray backslash.
  5. [Section 6, Theorem 6.1 and following paragraph] The caveat for θ=kπ/4 with odd k appears only after the main complexity conclusions. Please restate the O(ε^{-2}) claim as valid for generic θ, and give details of the numerical experiment that reports "up to an order of magnitude faster" convergence for the exceptional angles.

Circularity Check

0 steps flagged

No circularity found: the survey restates peer-reviewed scaling theorems; the challenged heuristic and the ε-rate issue are not reductions to inputs.

full rationale

The paper is a survey of scaling results for PDMC. Its main theorems (5.1, 6.1, Section 7) are attributed to published papers [13,14,2,8,17] with overlapping authorship, but they are presented as external theorems with explicit model assumptions (Gaussian targets, anisotropic Gaussian U_{θ,ε}, Bayesian big-data posteriors) rather than as consequences of the survey's own definitions. Restating one's own prior results in a survey is normal scholarly practice and, under the review rules, the citations are real evidence: the statements are mathematically checkable and are not assumptions that include the survey's conclusions. The only apparent heuristic generalization—'the ratio of expected number of refreshment jumps to overall jumps is 0.7812. The latter observation can be used more generally as a suitable criterion for tuning of the refreshment rate'—is an extrapolation from a Gaussian computation, not a fitted parameter renamed as a prediction, and it is not load-bearing for the paper's central complexity comparisons. The skeptical objection in §6 (switching rates from Eq. (1) should scale as ε^{-1/2}, not ε^{-1}) is an internal consistency or correctness concern about the bridge from Theorem 6.1 to the stated event-count complexities, not a circularity: it does not show that a claimed result is equivalent by construction to its inputs. Hence the circularity score is 0.

Axiom & Free-Parameter Ledger

2 free parameters · 4 axioms · 0 invented entities

No invented entities. The central quantities the reader is asked to take on faith are the numerically computed numbers (λ_r=1.424, ratio 0.7812, Ω_θ) and the two-timescale separation for anisotropic targets; the latter is the fragile assumption that carries the Section 6 conclusions.

free parameters (2)
  • Optimal refreshment rate λ_r=1.424 and refreshment-jump ratio 0.7812 = λ_r ≈ 1.424; ratio ≈ 0.7812
    Computed numerically from the semi-analytical σ²(λ_r) for a Gaussian target in Theorem 5.1(i)(b); the ratio is then asserted as a general tuning criterion for BPS without evidence beyond this example.
  • Angle-dependent diffusion speed Ω_θ for ZZP anisotropic limit = Depicted in Figure 2; closed form 'explicit (but complicated)' deferred to [14]
    The survey presents Ω_θ only graphically; without the closed form, the value at any θ cannot be checked from the survey text.
axioms (4)
  • domain assumption Stationarity construction: λ_i(x,v) = (v_i ∂_i U(x))_+ + γ_i with γ_i ≥ 0 independent of v (Eq. 1), and BPS bounce rate (⟨v,∇U⟩)_+ with reflection; these ensure π(dx,dv) is stationary with marginal π(dx).
    Used throughout Section 2 to define the samplers; correctness is referenced to [19,9] rather than proved in this survey.
  • domain assumption Exponential ergodicity conditions of Theorem 3.1 (coercive U, gradient growth conditions (a)–(d)); these justify the FCLT in Theorem 4.1 via the Glynn–Meyn framework [29].
    The FCLT and CLT in Section 4 inherit these conditions; they are stated but not proved here.
  • domain assumption Two-timescale separation in Section 6: the fast ridge coordinate y²_t equilibrates while the slow coordinate is nearly constant (“It turns out that y² quickly converges to its stationary distribution”), enabling the OU and ODE limits of Theorem 6.1.
    This is the load-bearing heuristic for the anisotropy scaling; rigorous justification is deferred to [14].
  • standard math Bernstein–von Mises concentration of the posterior around the mode x̂(n) at scale n^{-1/2} (Section 7.1–7.2), used to justify the control variate expansion and the n^{1/2} rescaling in the stationary phase.
    Invoked as a consequence of the Bernstein–von Mises theorem (cited as [41]); it underpins the big-data scaling conclusions.

pith-pipeline@v1.3.0-alltime-deepseek · 11888 in / 11958 out tokens · 123881 ms · 2026-08-01T04:40:48.793341+00:00 · methodology

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read the original abstract

Piecewise Deterministic Monte Carlo (PDMC) algorithms utilize continuous time Markov processes to generate samples from continuous distributions, and provide a modern alternative to discrete time Markov chain Monte Carlo algorithms. In this work we provide a survey of recent results on scaling limit arguments to understand the behaviour and efficiency of two often-used Piecewise Deterministic Monte Carlo algorithms: the Bouncy Particle Sampler and the Zig-Zag Process. In particular we discuss a Functional Central Limit Theorem, scaling in the high-dimensional regime, scaling under anisotropy, and scaling in the big data regime. This work is intended as part of the proceedings of the 2024 Isaac Newton Institute Programme "Stochastic systems for anomalous diffusion".

Figures

Figures reproduced from arXiv: 2607.22449 by Joris Bierkens.

Figure 1
Figure 1. Figure 1: σ 2 (λr) as a function of λr. The maximum is attained at λr = 1.424. (ii) For the ZZP, with V = {−1, +1} d , we have that, (a) for all values of d, the first coordinate process C d t is a one-dimensional Zig-Zag process. 9 [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The speed Ωθ of the diffusion scaling limit of the slow coordinate of the Zig-Zag process as a function of the angle θ of the anisotropic distribution with the x-axis. The main conclusions we can draw from Theorem 6.1 are the following. First, BPS does not require rescaling of time to attain its scaling limit. This is in contrast to the ZZP, which requires speeding-up by a factor ϵ −1 . Since the number of… view at source ↗
Figure 3
Figure 3. Figure 3: Trajectories for different versions of the Zig-Zag algorithm targeting a Bayesian [PITH_FULL_IMAGE:figures/full_fig_p015_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Asymptotic drift b(x) for different models and subsampling schemes in one dimension for three different choices of data generating distribution. In all cases the data is generated from the distribution in the caption with ‘true’ parameter x = 0. The black curve denotes the drift corresponding to the canonical rate λcan, the red curve corresponds to λˆ SS, and the blue curve corresponds to λˆCV. Note that i… view at source ↗

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Reference graph

Works this paper leans on

42 extracted references · 2 linked inside Pith

  1. [1]

    Sanket Agrawal, Joris Bierkens, Kengo Kamatani, and Gareth O. Roberts. Tran- sient regime of piecewise deterministic Monte Carlo algorithms.arXiv preprint arXiv:2509.16062, 2025

    arXiv 2025

  2. [2]

    Sanket Agrawal, Joris Bierkens, and Gareth O. Roberts. Large sample scal- ing analysis of the Zig-Zag algorithm for Bayesian inference.arXiv preprint arXiv:2411.14983, 2024

    Pith/arXiv arXiv 2024

  3. [3]

    Hypoco- ercivity of Piecewise Deterministic Markov Process-Monte Carlo.The Annals of Applied Probability, 31(5):2478–2517, 2021

    Christophe Andrieu, Alain Durmus, Nikolas N¨ usken, and Julien Roussel. Hypoco- ercivity of Piecewise Deterministic Markov Process-Monte Carlo.The Annals of Applied Probability, 31(5):2478–2517, 2021

    2021

  4. [4]

    Adaptive schemes for piecewise deterministic Monte Carlo algorithms.Bernoulli

    Andrea Bertazzi and Joris Bierkens. Adaptive schemes for piecewise deterministic Monte Carlo algorithms.Bernoulli. Official Journal of the Bernoulli Society for Mathematical Statistics and Probability, 28(4):2404–2430, 2022

    2022

  5. [5]

    Approximations of piecewise de- terministic markov processes and their convergence properties.Stochastic Processes and their Applications, 154:91–153, 2022

    Andrea Bertazzi, Joris Bierkens, and Paul Dobson. Approximations of piecewise de- terministic markov processes and their convergence properties.Stochastic Processes and their Applications, 154:91–153, 2022

    2022

  6. [6]

    Piecewise deterministic sampling with splitting schemes.Journal of Machine Learning Research, 26(243):1– 94, 2025

    Andrea Bertazzi, Paul Dobson, and Pierre Monmarch´ e. Piecewise deterministic sampling with splitting schemes.Journal of Machine Learning Research, 26(243):1– 94, 2025

    2025

  7. [7]

    Asymp- totic analysis of the random walk metropolis algorithm on ridged densities.Annals of Applied Probability, 28(5):2966–3001, 2018

    Alexandros Beskos, Gareth Roberts, Alexandre Thiery, and Natesh Pillai. Asymp- totic analysis of the random walk metropolis algorithm on ridged densities.Annals of Applied Probability, 28(5):2966–3001, 2018

    2018

  8. [8]

    Limit theorems for the zig-zag process.Ad- vances in Applied Probability, 49(3):791–825, July 2017

    Joris Bierkens and Andrew Duncan. Limit theorems for the zig-zag process.Ad- vances in Applied Probability, 49(3):791–825, July 2017

    2017

  9. [9]

    Joris Bierkens, Paul Fearnhead, and Gareth O. Roberts. The Zig-Zag Process and Super-Efficient Sampling for Bayesian Analysis of Big Data.Annals of Statistics, 47(3):1288–1320, 2019

    2019

  10. [10]

    Methods and applications of PDMP samplers with boundary conditions.arXiv preprint arXiv:2303.08023, 2023

    Joris Bierkens, Sebastiano Grazzi, Gareth Roberts, and Moritz Schauer. Methods and applications of PDMP samplers with boundary conditions.arXiv preprint arXiv:2303.08023, 2023

    Pith/arXiv arXiv 2023

  11. [11]

    A piecewise deterministic Monte Carlo method for diffusion bridges.Statistics and Computing, 31(3):37, April 2021

    Joris Bierkens, Sebastiano Grazzi, Frank van der Meulen, and Moritz Schauer. A piecewise deterministic Monte Carlo method for diffusion bridges.Statistics and Computing, 31(3):37, April 2021

    2021

  12. [12]

    Sticky PDMP samplers for sparse and local inference problems.Statistics and Computing, 33(1):8, November 2022

    Joris Bierkens, Sebastiano Grazzi, Frank van der Meulen, and Moritz Schauer. Sticky PDMP samplers for sparse and local inference problems.Statistics and Computing, 33(1):8, November 2022. 18

    2022

  13. [13]

    Joris Bierkens, Kengo Kamatani, and Gareth O. Roberts. High-dimensional scal- ing limits of piecewise deterministic sampling algorithms.The Annals of Applied Probability, 32(5):3361–3407, 2022

    2022

  14. [14]

    Joris Bierkens, Kengo Kamatani, and Gareth O. Roberts. Scaling of piecewise deterministic Monte Carlo for anisotropic targets.Bernoulli. Official Journal of the Bernoulli Society for Mathematical Statistics and Probability, 31(3):2323–2350, 2025

    2025

  15. [15]

    Large deviations for the empirical measure of the zig-zag process.The Annals of Applied Probability, 31(6):2811–2843, December 2021

    Joris Bierkens, Pierre Nyquist, and Mikola C Schlottke. Large deviations for the empirical measure of the zig-zag process.The Annals of Applied Probability, 31(6):2811–2843, December 2021

    2021

  16. [16]

    A piecewise deterministic scaling limit of lif- ted Metropolis–Hastings in the Curie–Weiss model.Annals of Applied Probability, 27(2):846–882, 2017

    Joris Bierkens and Gareth Roberts. A piecewise deterministic scaling limit of lif- ted Metropolis–Hastings in the Curie–Weiss model.Annals of Applied Probability, 27(2):846–882, 2017

    2017

  17. [17]

    Ergodicity of the zigzag process.Ann

    Joris Bierkens, Gareth O Roberts, and Pierre-Andr´ e Zitt. Ergodicity of the zigzag process.Ann. Appl. Probab., 29(4):2266–2301, 2019

    2019

  18. [18]

    Randomized Hamiltonian Monte Carlo.The Annals of Applied Probability, 27(4):2159–2194, 2017

    Nawaf Bou-Rabee and Jes´ us Mar ´ ıa Sanz-Serna. Randomized Hamiltonian Monte Carlo.The Annals of Applied Probability, 27(4):2159–2194, 2017

    2017

  19. [19]

    The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method.Journal of the American Statistical Association, 2017

    Alexandre Bouchard-Cˆ ot´ e, Sebastian J Vollmer, and Arnaud Doucet. The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method.Journal of the American Statistical Association, 2017

    2017

  20. [20]

    Alice Corbella, Simon E. F. Spencer, and Gareth O. Roberts. Automatic Zig-Zag sampling in practice.Statistics and Computing, 32(6):107, November 2022

    2022

  21. [21]

    M. H. A. Davis. Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models.Journal of the Royal Statistical Society. Series B (Methodological), 46(3):353–388, 1984

    1984

  22. [22]

    M. H. A. Davis.Markov Models and Optimization, volume 49. Chapman & Hall, London, 1993

    1993

  23. [23]

    Exponential ergodicity of the bouncy particle sampler.The Annals of Statistics, 47(3):1268– 1287, 2019

    George Deligiannidis, Alexandre Bouchard-Cˆ ot´ e, and Arnaud Doucet. Exponential ergodicity of the bouncy particle sampler.The Annals of Statistics, 47(3):1268– 1287, 2019

    2019

  24. [24]

    Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates.The Annals of Applied Prob- ability, 31(6):2612–2662, 2021

    George Deligiannidis, Daniel Paulin, Alexandre Bouchard-Cˆ ot´ e, and Arnaud Doucet. Randomized Hamiltonian Monte Carlo as scaling limit of the bouncy particle sampler and dimension-free convergence rates.The Annals of Applied Prob- ability, 31(6):2612–2662, 2021

    2021

  25. [25]

    Hypocoercivity for lin- ear kinetic equations conserving mass.Transactions of the American Mathematical Society, 367(6):3807–3828, February 2015

    Jean Dolbeault, Cl´ ement Mouhot, and Christian Schmeiser. Hypocoercivity for lin- ear kinetic equations conserving mass.Transactions of the American Mathematical Society, 367(6):3807–3828, February 2015. 19

    2015

  26. [26]

    Geometric ergodicity of the bouncy particle sampler.The Annals of Applied Probability, 30(5):2069–2098, 2020

    Alain Durmus, Arnaud Guillin, and Pierre Monmarch´ e. Geometric ergodicity of the bouncy particle sampler.The Annals of Applied Probability, 30(5):2069–2098, 2020

    2069

  27. [27]

    Piecewise deterministic Markov processes and their invariant measures.Annales de l’Institut Henri Poincar´ e (B) Probabilit´ es et Statistiques, 57(3):1442–1475, 2021

    Alain Durmus, Arnaud Guillin, and Pierre Monmarch´ e. Piecewise deterministic Markov processes and their invariant measures.Annales de l’Institut Henri Poincar´ e (B) Probabilit´ es et Statistiques, 57(3):1442–1475, 2021

    2021

  28. [28]

    Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo.Statist

    Paul Fearnhead, Joris Bierkens, Murray Pollock, and Gareth O Roberts. Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo.Statist. Sci., 33(3):386–412, 2018

    2018

  29. [29]

    Glynn and Sean P

    Peter W. Glynn and Sean P. Meyn. A Liapounov bound for solutions of the poisson equation.Annals of Probability, 24(2):916–931, 1996

    1996

  30. [30]

    Cores for piecewise-deterministic Markov processes used in Markov chain Monte Carlo.Electronic Communications in Probability, 26(none):1– 12, 2021

    Peter Holderrieth. Cores for piecewise-deterministic Markov processes used in Markov chain Monte Carlo.Electronic Communications in Probability, 26(none):1– 12, 2021

    2021

  31. [31]

    Michel, S

    M. Michel, S. C. Kapfer, and W. Krauth. Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps.The Journal of Chemical Physics, 140(5), 2014

    2014

  32. [32]

    Forward event-chain Monte Carlo: Fast sampling by randomness control in irreversible Markov chains.Journal of Computational and Graphical Statistics, 29(4):689–702, 2020

    Manon Michel, Alain Durmus, and St´ ephane S´ en´ ecal. Forward event-chain Monte Carlo: Fast sampling by randomness control in irreversible Markov chains.Journal of Computational and Graphical Statistics, 29(4):689–702, 2020

    2020

  33. [33]

    ´ etude spectrale minutieuse de processus moins ind´ ecis que les autres

    Laurent Miclo and Pierre Monmarch´ e. ´ etude spectrale minutieuse de processus moins ind´ ecis que les autres. In Catherine Donati-Martin, Antoine Lejay, and Alain Rouault, editors,S´ eminaire de Probabilit´ es XL V, pages 459–481. Springer Interna- tional Publishing, Heidelberg, 2013

    2013

  34. [34]

    Monmarch´ e

    P. Monmarch´ e. Piecewise deterministic simulated annealing.ALEA, 13(1):357–398, 2016

    2016

  35. [35]

    Hypocoercive relaxation to equilibrium for some kinetic models

    Pierre Monmarch´ e. Hypocoercive relaxation to equilibrium for some kinetic models. Kinetic and Related Models, 7(2):341–360, 2014

    2014

  36. [36]

    NuZZ: Numerical Zig-Zag for general models.Statistics and Computing, 34(1):61, January 2024

    Filippo Pagani, Augustin Chevallier, Sam Power, Thomas House, and Simon Cotter. NuZZ: Numerical Zig-Zag for general models.Statistics and Computing, 34(1):61, January 2024

    2024

  37. [37]

    E. A. J. F. Peters and G. De With. Rejection-free Monte Carlo sampling for general potentials.Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 85(2):1–5, 2012

    2012

  38. [38]

    G. O. Roberts, A. Gelman, and W. R. Gilks. Weak convergence and optimal scaling of random walk Metropolis algorithms.Annals of Applied Probability, 7(1):110–120, 1997. 20

    1997

  39. [39]

    G. O. Roberts and J. S. Rosenthal. Optimal scaling of discrete approximations to Langevin diffusions.Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60(1):255–268, 1998

    1998

  40. [40]

    Diffusive Scaling Limits of Forward Event- Chain Monte Carlo: Provably Efficient Exploration with Partial Refreshment.arXiv preprint arXiv:2602.17087, 2026

    Hirofumi Shiba and Kengo Kamatani. Diffusive Scaling Limits of Forward Event- Chain Monte Carlo: Provably Efficient Exploration with Partial Refreshment.arXiv preprint arXiv:2602.17087, 2026

    arXiv 2026

  41. [41]

    Cambridge University Press, Cambridge, 1998

    A W van der Vaart.Asymptotic Statistics, volume 3. Cambridge University Press, Cambridge, 1998

    1998

  42. [42]

    Coordinate sampler: A non-reversible Gibbs- like MCMC sampler.Statistics and Computing, 30(3):721–730, 2020

    Changye Wu and Christian P Robert. Coordinate sampler: A non-reversible Gibbs- like MCMC sampler.Statistics and Computing, 30(3):721–730, 2020. 21

    2020