Limit laws for transient random walks in random environment on $\z$
arXiv:math/0703660
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 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.
31 pages, accepted for publication in "Annales de l'Institut Fourier"