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

Nathanaël Enriquez·Christophe Sabot·Olivier Zindy
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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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Nathanaël Enriquez, Christophe Sabot, Olivier Zindy. 2009-04-09. Limit laws for transient random walks in random environment on $\z$. https://arxiv.org/abs/math/0703660

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