Related papers: Exact Coupling of Random Walks on Polish Groups

We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found…

Two infinite walks on the same finite graph are called compatible if it is possible to introduce delays into them in such a way that they never collide. Years ago, Peter Winkler asked the question: for which graphs are two independent walks…

In the eighties, A. Connes and E. J. Woods made a connection between hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks. The present paper explains this connection and gives a detailed proof of two…

We study random walk on complex networks with transition probabilities which depend on the current and previously visited nodes. By using an absorbing Markov chain we derive an exact expression for the mean first passage time between pairs…

A random walk in a sparse random environment is a model introduced by Matzavinos et al. [Electron. J. Probab. 21, paper no. 72: 2016] as a generalization of both a simple symmetric random walk and a classical random walk in a random…

This paper considers an infinite system of instantaneously coalescing rate one simple random walks on $\mathbb{Z}^2$, started from the initial condition with all sites in $\mathbb{Z}^2$ occupied. We show that the correlation functions of…

We consider a model of space-continuous one-dimensional random walk with simple correlation between the steps: the probability that two consecutive steps have same sign is $q$ with $0\leq q\leq 1$. The parameter $q$ allows thus to control…

We study the probability that certain laws are satisfied on infinite groups, focusing on elements sampled by random walks. For several group laws, including the metabelian one, we construct examples of infinite groups for which the law…

We prove a conjecture raised by the work of Diaconis and Shahshahani (1981) about the mixing time of random walks on the permutation group induced by a given conjugacy class. To do this we exploit a connection with coalescence and…

The paper is concerned with a class of two-sided stochastic processes of the form $X=W+A$. Here $W$ is a two-sided Brownian motion with random initial data at time zero and $A\equiv A(W)$ is a function of $W$. Elements of the related…

When it comes to random walk on the integers $\mathbb{Z}$, the arguably first step of generalization beyond simple random walk is the class of one-sidedly continuous random walk, where the stepsize in only one direction is bounded by 1.…

We analyze a class of continuous time random walks in $\mathbb R^d,d\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes…

Let $b$ be an integer greater than 1 and let $W^{\ee}=(W^{\ee}_n; n\geq 0)$ be a random walk on the $b$-ary rooted tree $\U_b$, starting at the root, going up (resp. down) with probability $1/2+\epsilon$ (resp. $1/2 -\epsilon$), $\epsilon…

The Brownian Web (BW) is a family of coalescing Brownian motions starting from every point in space and time $\R\times\R$. It was first introduced by Arratia, and later analyzed in detail by T\'{o}th and Werner. More recently, Fontes,…

We study a system of coalescing continuous-time random walks starting from every site on $\mathbb{Z}$, where the jump increments lie in the domain of attraction of an $\alpha$-stable distribution with $\alpha\in(0,1]$. We establish sharp…

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed…

We give new criteria for ballistic behavior of random walks in random environment which are perturbations of the simple symmetric random walk on $\mathbb Z^d$ in dimensions $d\ge 4$. Our results extend those of Sznitman [Ann. Probab. 31,…

In [3] the radius of convergence of the generating function of the collision local time of two independent copies of an irreducible, symmetric and transient random walk on Zd, d \geq 1, was studied. Two versions were considered: z1, the…

Coalescing random walks is a fundamental stochastic process, where a set of particles perform independent discrete-time random walks on an undirected graph. Whenever two or more particles meet at a given node, they merge and continue as a…

The rotor walk on a graph is a deterministic analogue of random walk. Each vertex is equipped with a rotor, which routes the walker to the neighbouring vertices in a fixed cyclic order on successive visits. We consider rotor walk on an…