Related papers: Non-trivial linear bounds for a random walk driven…

Exclusion processes became paradigmatic models of nonequilibrium interacting particle systems of wide range applicability both across the natural and the applied, social and technological sciences. Usually they are defined as a…

We consider a random walk on a second countable locally compact topological space endowed with an invariant Radon measure. We show that if the walk is symmetric and if every subset which is invariant by the walk has zero or infinite…

We focus on the existence and characterization of the limit for a certain critical branching random walks in time-space random environment in one dimension which was introduced by M. Birnkenr et.al. Each particle performs simple random walk…

We give criteria for ergodicity, transience and null recurrence for the random walk in random environment on {0,1,2,...}, with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results…

We consider simple exclusion processes on Z for which the underlying random walk has a finite first moment and a non-zero mean and whose initial distributions are product measures with different densities to the left and to the right of the…

The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are…

We consider a random walk X_n in non-i.i.d. environment and show that the ratio of log X_n to log n converges in probability to a positive constant.

We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider…

Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…

Consider a family of random ordered graph trees $(T_n)_{n\geq 1}$, where $T_n$ has $n$ vertices. It has previously been established that if the associated search-depth processes converge to the normalised Brownian excursion when rescaled…

We prove the annealed Central Limit Theorem for random walks in bistochastic random environments on $Z^d$ with zero local drift. The proof is based on a "dynamicist's interpretation" of the system, and requires a much weaker condition than…

We characterize ballistic behavior for general i.i.d. random walks in random environments on $\mathbb{Z}$ with bounded jumps. The two characterizations we provide do not use uniform ellipticity conditions. They are natural in the sense that…

We study exit laws from large balls in $\mathbb{Z}^d$, $d\geq3$, of random walks in an i.i.d. random environment that is a small perturbation of the environment corresponding to simple random walk. Under a centering condition on the measure…

In the present paper, as a continuation of our preceding paper [10], we study another kind of central limit theorems (CLTs) for non-symmetric random walks on nilpotent covering graphs from a viewpoint of discrete geometric analysis…

In this short note, we prove that $v(-\epsilon)=-v(\epsilon)$. Here, $v(\epsilon)$ is the speed of a one-dimensional random walk in a dynamic \emph{reversible} random environment, that jumps to the right (resp. to the left) with probability…

We consider simple random walk on Z^d, d bigger or equal to 3. Motivated by the work of A.-S. Sznitman and the author in arXiv:1304.7477 and arXiv:1310.2177, we investigate the asymptotic behaviour of the probability that a large body gets…

We study boundaries arising from limits of ratios of transition probabilities for random walks on relatively hyperbolic groups. We extend, as well as determine significant limitations of, a strategy employed by Woess for computing…

We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely…

We consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…

A sufficient condition for the uniqueness of multinomial sequential unbiased estimators is provided generalizing a classical result for binomial samples. Unbiased estimators are applied to infer the parameters of multidimensional or…