Quenched limits for the fluctuations of transient random walks in random environment on Z

Nathanaël Enriquez, Christophe Sabot, Laurent Tournier, Olivier Zindy

Published 2010-12-09, updated 2013-04-15Version 3

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].