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Article Dans Une Revue The Annals of Applied Probability Année : 2013

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. The Annals of Applied Probability, 2013, 23 (3), pp.1148-1187. ⟨10.1214/12-AAP867⟩. ⟨hal-00543882v3⟩
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