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.

31 pages, accepted for publication in "Annales de l'Institut Fourier"

References in corpus (5)

• Single Molecule Statistics and the Polynucleotide Unzipping Transition
• Quenched limits for transient, zero speed one-dimensional random walk in random environment
• Reconstructing a Random Potential from its Random Walks
• Simple Transient Random Walks in One-dimensional Random Environment: the Central Limit Theorem
• Universality of the REM for dynamics of mean-field spin glasses

Cited by in corpus (6)

• Quenched limits for transient, zero speed one-dimensional random walk in random environment
• On slowdown and speedup of transient random walks in random environment
• Biased random walks on a Galton-Watson tree with leaves
• Scaling limit and aging for directed trap models
• Law of large numbers for a finite-range random walk in a dynamic random environment with nonuniform mixing
• Maximal Displacement for Bridges of Random Walks in a Random Environment