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Pré-Publication, Document De Travail Année : 2012

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

Résumé

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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Dates et versions

hal-00543882 , version 1 (07-12-2010)
hal-00543882 , version 2 (01-04-2012)
hal-00543882 , version 3 (19-09-2013)

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Nathanaël Enriquez, Christophe Sabot, Laurent Tournier, Olivier Zindy. Quenched limits for the fluctuations of transient random walks in random environment on Z. 2012. ⟨hal-00543882v2⟩

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