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

Abstract : 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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Ann. Appl. Probab., 2013, 23 (3), pp.1148-1187. <10.1214/12-AAP867>
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Soumis le : jeudi 19 septembre 2013 - 10:54:02
Dernière modification le : jeudi 16 mars 2017 - 01:07:44

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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. Ann. Appl. Probab., 2013, 23 (3), pp.1148-1187. <10.1214/12-AAP867>. <hal-00543882v3>

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