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


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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.



Author: Nathanaël Enriquez; Christophe Sabot; Laurent Tournier; Olivier Zindy

Source: https://archive.org/



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