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

2007/03/22 by Nathanaël Enriquez, Enriquez, Nathanaël, Christophe Sabot +3 · 2 citations
Mathematics · Physics and Astronomy · Biochemistry, Genetics and Molecular Biology · #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #Diffusion and Search Dynamics

paper · pdf · doi:10.48550/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 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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• Maximal Displacement for Bridges of Random Walks in a Random Environment
• Quenched scaling limit for biased random walks on random, heavy tailed conductances: low dimensions

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