相关论文: Gumbel laws in the symmetric exclusion process

The uniform spanning tree (UST) and the loop-erased random walk (LERW) are related probabilistic processes. We consider the limits of these models on a fine grid in the plane, as the mesh goes to zero. Although the existence of scaling…

We consider a class of branching-selection particle systems on $\R$ similar to the one considered by E. Brunet and B. Derrida in their 1997 paper "Shift in the velocity of a front due to a cutoff". Based on numerical simulations and…

Adding quenched disorder to the one-dimensional asymmetric exclusion process is known to always induce phase separation. To test the robustness of this result, we introduce two modifications of the process that allow particles to bypass…

We consider the persistent exclusion process in which a set of persistent random walkers interact via hard-core exclusion on a hypercubic lattice in $d$ dimensions. We work within the ballistic regime whereby particles continue to hop in…

Consider $M_n$ the maximal position at generation $n$ of a supercritical branching random walk. A\"id\'ekon (2013) obtained and described the convergence in law, as time $n$ goes to infinity, of $M_n-m_n$, where $m_n$ is an explicit…

Spontaneous symmetry breaking is a fundamental notion in modern physics, ranging from high energy to condensed matter. However, the usual spontaneous symmetry breaking only considers the equal probability to select the vacua. In this work,…

In this paper, we considier the limiting distribution of the maximum interpoint Euclidean distance $M_n=\max _{1 \leq i<j \leq n}\left\|\boldsymbol{X}_i-\boldsymbol{X}_j\right\|$, where $\boldsymbol{X}_1, \boldsymbol{X}_2, \ldots,…

We consider a system consisting of a planar random walk on a square lattice, submitted to stochastic elementary local deformations. Depending on the deformation transition rates, and specifically on a parameter $\eta$ which breaks the…

We consider nearest neighbour spatial random permutations on $\mathbb{Z}^d$. In this case, the energy of the system is proportional the sum of all cycle lengths, and the system can be interpreted as an ensemble of edge-weighted, mutually…

In the framework of Cramer's probabilistic model of primes, we explore the exact and asymptotic distributions of maximal prime gaps. We show that the Gumbel extreme value distribution exp(-exp(-x)) is the limit law for maximal gaps between…

We establish the incompressible limit of weakly asymmetric simple exclusion processes coupled through particle collisions. The incompressible limit depends on various parameters in the particle system and is linked to fluid dynamics…

We consider discrete-time branching random walks with a radially symmetric distribution. Independently of each other individuals generate offspring whose relative locations are given by a copy of a radially symmetric point process…

The Gumbel trick is a method to sample from a discrete probability distribution, or to estimate its normalizing partition function. The method relies on repeatedly applying a random perturbation to the distribution in a particular way, each…

This paper enhances the result of the work [G. Kozma, B. T\'oth, Ann. Probab. vol. 45 (2017) 4307-4347] . We prove the central limit theorem (in probability w.r.t. the environment) for the displacement of a random walker in divergence-free…

The study of discrete-time stochastic processes on the half-line with mean drift at $x$ given by $\mu_1 (x) \to 0$ as $x \to \infty$ is known as Lamperti's problem. We give sharp almost-sure bounds for processes of this type in the case…

The subcritical Markov branching process X(t) starting with one particle as the initial condition has the ultimate extinction probability q = 1. The branching mechanism in consideration is defined by the mixture of logarithmic distributions…

We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant…

We consider particle systems in locally compact Abelian groups with particles moving according to a process with symmetric stationary independent increments and undergoing one and two levels of critical branching. We obtain long time…

We consider the symmetric simple exclusion processes with a slow site in the discrete torus with $n$ sites. In this model, particles perform nearest-neighbor symmetric random walks with jump rates everywhere equal to one, except at one…

The purpose of this paper is to study a one-dimensional polymer penalized by its range and placed in a random environment $\omega$. The law of the simple symmetric random walk up to time $n$ is modified by the exponential of the sum of…