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Journal Articles Annales de l'Institut Fourier Year : 2009

Limit laws for transient random walks in random environment on $\z$

Abstract

We consider transient random walks in random environment on $\z$ with zero asymptotic speed. A classical result of Kesten, Kozlov and Spitzer says that the hitting time of the level $n$ converges in law, after a proper normalization, towards a positive stable law, but they do not obtain a description of its parameter. A different proof of this result is presented, that leads to a complete characterization of this stable law. The case of Dirichlet environment turns out to be remarkably explicit.
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Dates and versions

hal-00137770 , version 1 (21-03-2007)
hal-00137770 , version 2 (06-11-2007)
hal-00137770 , version 3 (25-01-2008)
hal-00137770 , version 4 (09-04-2009)

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Nathanaël Enriquez, Christophe Sabot, Olivier Zindy. Limit laws for transient random walks in random environment on $\z$. Annales de l'Institut Fourier, 2009, 59, pp.2469-2508. ⟨hal-00137770v4⟩
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