Related papers: Variable speed symmetric random walk driven by sym…
We introduce a model for the slow relaxation of an energy landscape caused by its local interaction with a random walker whose motion is dictated by the landscape itself. By choosing relevant measures of time and potential this…
We are interested in the randomly biased random walk on the supercritical Galton--Watson tree. Our attention is focused on a slow regime when the biased random walk $(X_n)$ is null recurrent, making a maximal displacement of order of…
We present a comprehensive classification of one-dimensional coined quantum walks on the infinite line, focusing on the spatial probability distributions they induce. Building on prior results, we identify all initial coin states that lead…
In this paper we prove a rate of escape theorem and a central limit theorem for isotropic random walks on Fuchsian buildings, giving formulae for the speed and asymptotic variance. In particular, these results apply to random walks induced…
We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit characterization of the action functional. The random medium…
We consider random walks perturbed at zero which behave like (possibly different) random walks with i.i.d. increments on each half lines and restarts at $0$ whenever they cross that point. We show that the perturbed random walk, after being…
We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase…
Attributing a positive value \tau_x to each x in Z^d, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (\tau_x), often known as "Bouchaud's trap model". We assume that these weights are…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study…
We consider transient one-dimensional random walks in random environment with zero asymptotic speed. An aging phenomenon involving the generalized Arcsine law is proved using the localization of the walk at the foot of "valleys" of height…
We investigate random walks on the general linear group constrained within a specific domain, with a focus on their asymptotic behavior. In a previous work [38], we constructed the associated harmonic measure, a key element in formulating…
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 study the motion of a random walker in one longitudinal and d transverse dimensions with a quenched power law correlated velocity field in the longitudinal x-direction. The model is a modification of the Matheron-de Marsily (MdM) model,…
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 show that one-dimensional random walks in a quasi-periodic environment with Liouville frequency generically have an erratic statistical behavior. In the recurrent case we show that neither quenched nor annealed limit theorems hold and…
We prove that the speed of a biased random walk on a supercritical Galton-Watson tree conditioned to survive is analytic within the ballistic regime. This extends the previous work arXiv:1906.07913 in which it was shown that the speed is…
We prove a shape theorem and derive a variational formula for the limiting quenched Lyapunov exponent and the Green's function of random walk in a random potential on a square lattice of arbitrary dimension and with an arbitrary finite set…
We consider the nearest-neighbor simple random walk on $\Z^d$, $d\ge2$, driven by a field of i.i.d. random nearest-neighbor conductances $\omega_{xy}\in[0,1]$. Apart from the requirement that the bonds with positive conductances percolate,…
We propose a new approach for finding discrete harmonic functions in the quarter plane with Dirichlet conditions. It is based on solving functional equations that are satisfied by the generating functions of the values taken by the harmonic…