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

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

2010-12-09

arxiv.org/abs/1012.1959v2

Mathematics

Probability

This reviewed version was accepted for publication in Annals of Applied Probability

Scientific paper

We consider transient nearest-neighbour 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 (1975).

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