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1657 papers in math.PR · page 12
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Random walk clusters scale chemical distance as L (ln L)^{1/4}
Fractals of Simple Random Walks in Two Dimensions: A Monte Carlo Study
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Critical long-range walks converge to Brownian motion with log scaling
Quantitative stochastic homogenization for long-range random walks with critical jump index
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Critical long-range jumps yield Brownian motion under sqrt(t log t) scaling
Quantitative homogenization for the critical long-range random conductance model
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IDLA fluctuations on cylinders converge to Gaussian free field
Gaussian fluctuations for Internal DLA on cylinders
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Southwest boundary yields explicit tail bounds for random variable functions
Tail Bounds via Southwest Boundary
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Penrose tiling graph has independent set density (57-25√5)/2
A Nearest-Neighbor Hard-Core Model on a Penrose Graph
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Bochner integration built for random normed modules
A Bochner-type integration theory for random normed modules
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Graph RD equations converge to graphon limits
Graphon Limits of Graph Reaction--Diffusion Equations
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Closed-set large-deviation bounds fail without tail control
Failure of ambient closed-set large-deviation upper bounds in entropic optimal transport
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Uniqueness transition proven for random-cluster on trees
Uniqueness and Mixing in the Low-Temperature Random-Cluster Model on Trees and Random Graphs
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Lower bound on TAP complexity matches Parisi Legendre prediction
The Legendre structure of the TAP complexity for the Ising spin glass
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Framework defines moments for distributions without them
Distributional Statistical Models: Weak Moments, Cumulants, and a Central Limit Theorem
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Weak moments define a central limit theorem for heavy-tailed laws
Distributional Statistical Models: Weak Moments, Cumulants, and a Central Limit Theorem
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Ising model on two-community graphs has uniqueness phase transition
The Ising Model on a Two-Community Stochastic Block Model
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Two-community Ising model has non-unique Gibbs phase transition
The Ising Model on a Two-Community Stochastic Block Model
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SMC jump chain ergodic geometrically
Rates of forgetting for the sequentially Markov coalescent
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Perturbed twisted Toeplitz matrices yield 2D eigenvalue limits
Structured perturbations of tridiagonal twisted Toeplitz matrices
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E-processes deliver power-one tests for monotonicity and unimodality
E-values and sequential power-one tests for monotonicity and unimodality
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Random 0/1 polytopes expand edges linearly in dimension
The Mihail-Vazirani conjecture and strong edge-expansion in random $0/1$ polytopes
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Random loop model on sparse graphs has macroscopic loops above density threshold
Macroscopic loops in the random loop model on sparse random graphs
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Negative invasion rates imply extinction under relaxed bounds
Stochastic Extinction with Relaxed Boundedness Conditions
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Doob transform yields consistent estimators for composite births
Likelihood-based inference for birth-death processes with composite birth mechanisms
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Lévy fields build exact Wightman quantum fields for d >= 4
Direct construction of scalar quantum fields by L{\'e}vy fields -- nontrivial exact Wightman fields in a wider field with a relaxed G{\aa}rding-Wightman Axioms-
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This paper proves a central limit theorem for the smoothed count of holes in the Wiener…
Persistent Homology of the Wiener Sausage II: A Central Limit Theorem for Drifted Planar Brownian Motion
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Match test function regularity to drift to improve weak error rates
Weak error for SDEs with additive stable noise and singular drift: choose the test function in the same space as the drift!
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Small-rho expansion adds leverage to barrier pricing in clock volatility models
Extrema, Barrier Options, and Semi-Analytic Leverage Corrections in Stochastic-Clock Volatility Models
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Markov chain comparison yields universal edge statistics for sparse matrices
Edge Universality for Inhomogeneous Random Matrices II: Markov Chain Comparison and Critical Statistics
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Time-varying barriers tighten safety bounds for systems with dynamic obstacles
Stochastic Barrier Certificates in the Presence of Dynamic Obstacles
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Integral condition characterizes stochastic completeness on manifolds
Nonlocal Characterizations of Stochastic Completeness on Complete Riemannian Manifolds
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Random recursive tree heights decay polynomially upward and stretched-exponentially down
Atypical Decay Rates for Atypical Heights in Random Recursive Trees
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Super-Brownian motion persists in weak random environments for d at least 3
Persistence and local extinction for superprocesses in random environments
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Symmetric starts make spiked-matrix Langevin mix in log N time below criticality
Mixing times of Langevin dynamics for spiked matrix models
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Langevin dynamics on spiked matrices mix fast from symmetric starts
Mixing times of Langevin dynamics for spiked matrix models
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Summed SNR from mixed hyperedges crosses detection threshold
Achieving the Kesten-Stigum bound in the non-uniform hypergraph stochastic block model
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Viscous HJ homogenization error bounded by ε log(t/ε)
Sharp global and almost everywhere convergence rates for periodic homogenization of viscous quadratic Hamilton-Jacobi equations
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Selected problems bridge intuition and formal probability
Designing for the Development of Probabilistic Thinking: A Design-Based Research Study in Lower Secondary Education
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Lévy fluctuation identities survive general killing via new scale functions
Fluctuation theory for spectrally negative L\'evy processes killed by additive functionals
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Covariance fixed points split NN functionals into three limit regimes
Phase Transitions in the Fluctuations of Functionals of Random Neural Networks
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Ultrametric OGP bounds match RDT at successive levels
Ultrametric OGP - parametric RDT \emph{symmetric} binary perceptron connection
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Polynomial McKean-Vlasov SDEs give unique solutions for SIS epidemics
On McKean-Vlasov SDEs with polynomial drifts for SIS epidemic models
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Littlewood maxima obey exact liminf -(3 pi^2 /4)^{1/3} in (log log n)^{1/3} scale
On the maxima of Littlewood polynomials on $[-1,1]$
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Risk-averse operators gain from sharing CO2 storage risks
Risk sharing in cooperative game models for CO$_2$ storage with uncertain geology and pressure competition
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Split-merge on expanding intervals yields continuous point limits
Split merge dynamics for expanding intervals and point processes on the real line
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Stochastic convergence extended to Orlicz-Sobolev spaces
Stochastic $\Sigma$-convergence in Orlicz setting and Applications
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Entrance measures exist for expanding time-inhomogeneous McKean-Vlasov SDEs
Entrance measures and dynamics for time-inhomogeneous McKean-Vlasov stochastic differential equations
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Rectangles in growing network converge to stick-breaking limit
Growing random planar network with oriented branching and fusion
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Hierarchical disorder enables localization in any dimension
Anderson Localization for the hierarchical Anderson-Bernoulli model on $\mathbb{Z}^d$
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Cubic momentum rule reproduces periodic bubble-crash cycles
Dynamics of Periodic Bubbles and Crashes: Modeling Market Overheating and Panic Selling via Cubic Momentum
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Pesin formula equates SRB entropy to sum of positive Lyapunov exponents
Multifractal Analysis, Liv\v{s}ic Rigidity, and Fluctuation Theorems for Axiom A Diffeomorphisms: The Pesin Formula and the Gallavotti-Cohen Symmetry
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Spectral gap yields explicit mixing
Statistical Limit Theorems for Axiom A Diffeomorphisms: Exponential Mixing, Central Limit Theorem, and Large Deviations