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The study of random walk in random evolving environment has attracted much attention lately. The basic idea is that, due to the time mixing properties of the environment, the CLT should hold in any ...
We consider excited random walk on a strip. We assume that the cookies are positive and that the total expected drift per site is less than 1/L where L is the width of the strip. We prove a quenched...
Asymptotic Analysis of a Random Walk on a Hypercube with Many Dimensions。
MODERATE GROWTH AND RANDOM WALK ON FINITE GROUPS.
An Application of Harnack Inequalitise to Random Walk on Nilpotent Quotients。
We consider directed random walk on the infinite percolation cluster generated by supercritical oriented percolation, or equivalently the space-time embedding of the `ancestral lineage' of an individu...
Abstract: Consider a random walk $S_n=\sum_{i=0}^n X_i$ with negative drift. This paper deals with upper bounds for the maximum $M=\max_{n\ge 1}S_n$ of this random walk in different settings of power ...
Abstract: It is proved that the Green's function of a symmetric finite range random walk on a co-compact Fuchsian group decays exponentially in distance at the radius of convergence R. It is also show...
Abstract: We show how to compute the probabilities of various connection topologies for uniformly random spanning trees on graphs embedded in surfaces. As an application, we show how to compute the "i...
Abstract: Considering a critical branching random walk on the real line. In a recent paper, Aidekon [3] developed a powerful method to obtain the convergence in law of its minimum after a log-factor n...
Abstract: Consider the branching simple random walk on Z^d indexed by a critical geometric Galton-Watson tree conditioned to survive. Using the concept of unimodular random graphs, we show that the wa...
Abstract: For a symmetric, homogeneous and irreducible random walk on d-dimensional integer lattice Z^d, having zero mean and a finite variance of jumps, we study the passage times (with possible infi...
Abstract: We study the biased random walk in positive random conductances on $\mathbb{Z}^d$. This walk is transient in the direction of the bias. Our main result is that the random walk is ballistic i...
In this paper, we reveal the branching structure for a non-homogeneous random walk with bounded jumps. The ladder time T1, the first hitting time of [1,∞) by the walk starting from 0, could be expres...
all ( ,F1,P,X,F) the canonical space for the standard random walk on Z. Thus, denotes the set of paths  : N ! Z such that |(n + 1) − (n)| = 1, X = (Xn, n  0) is the canonical coordinate proc...

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