Quenched limits for the fluctuations of transient random walks in random environment on Z
Abstract
We consider transient nearest-neighbor random walks in random environment on Z. For a set of environments whose probability is converging to 1 as time goes to infinity, we describe the fluctuations of the hitting time of a level n, around its mean, in terms of an explicit function of the environment. Moreover, their limiting law is described using a Poisson point process whose intensity is computed. This result can be considered as the quenched analog of the classical result of Kesten, Kozlov and Spitzer [Compositio Math. 30 (1975) 145-168].
Keywords
Cite
@article{arxiv.1012.1959,
title = {Quenched limits for the fluctuations of transient random walks in random environment on Z},
author = {Nathanaël Enriquez and Christophe Sabot and Laurent Tournier and Olivier Zindy},
journal= {arXiv preprint arXiv:1012.1959},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AAP867 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: substantial text overlap with arXiv:1004.1333