Related papers: Precise large deviations for random walk in random…

We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…

In this paper, we consider directed polymers in random environment with long range jumps in discrete space and time. We extend to this case some techniques, results and classifications known in the usual short range case. However, some…

The quenched and annealed large deviations of the random walk in random environment are shown to conform on any compact set whenever the level of disorder is sufficiently low. In this work, we show that these two large deviations always…

Let $\Gamma$ be a countable group acting on a geodesic hyperbolic metric space $X$ and $\mu$ a probability measure on $\Gamma$ which generates a non elementary semi-group. Under the necessary assumption that $\mu$ has a finite exponential…

The statistics of persistent events, recently introduced in the context of phase ordering dynamics, is investigated in the case of the 1D lattice random walk in discrete time. We determine the survival probability of the random walker in…

We consider one dimensional random walks in random environment where every time the process stays at a location, it dies with a fixed probability. Under some mild assumptions it is easy to show that the survival probability goes to zero as…

In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the…

We consider a random walk in a fixed Z environment composed of two point types: (q,1-q) and (p,1-p) for 1/2<q<p. We study the expected hitting time at N for a given number k of p-drifts in the interval [1,N-1], and find that this time is…

We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle is proved in the scheme of series where the size of…

We consider a random walk on $\Z$ that branches at the origin only. In the supercritical regime we establish a law of large number for the maximal position $M_n$. Then we determine all possible limiting law for the sequence $M_n -\alpha n$…

We present large deviations estimates in the supremum norm for a system of independent random walks superposed with a birth-and-death dynamics evolving on the discrete torus with $N$ sites. The scaling limit considered is the so-called…

We consider a one-dimensional simple symmetric exclusion process in equilibrium, constituting a dynamic random environment for a nearest-neighbor random walk that on occupied/vacant sites has two different local drifts to the right. We…

We investigate a branching random walk where the displacements are independent from the branching mechanism and have a stretched exponential distribution. We describe the positions of the particles in the vicinity of the rightmost particle…

We consider the general branching random walk under minimal assumptions, which in particular guarantee that the empirical particle distribution admits an almost sure central limit theorem. For such a process, we study the large time decay…

We consider a bounded step size random walk in an ergodic random environment with some ellipticity, on an integer lattice of arbitrary dimension. We prove a level 3 large deviation principle, under almost every environment, with rate…

We study arithmetic properties of short uniform random walks in arbitrary dimensions, with a focus on explicit (hypergeometric) evaluations of the moment functions and probability densities in the case of up to five steps. Somewhat to our…

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a function of its summands as their number tends to infinity. In the large deviation range of the…

We study an agent-based model of animals marking their territory and evading adversarial territory in one dimension, with respect to the distribution of the size of the resulting territories. In particular, we use sophisticated sampling…

We consider a discrete-time random walk on the nodes of an unbounded hexagonal lattice. We determine the probability generating functions, the transition probabilities and the relevant moments. The convergence of the stochastic process to a…

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…