A law of large numbers for random walks in random mixing environments

2002/05/28 by Francis Comets, Comets, Francis, Ofer Zeitouni +1
Economics, Econometrics and Finance · Mathematics · #Markov Chains and Monte Carlo Methods #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60K40 #msc:82D30

paper · pdf · doi:10.48550/arxiv.math/0205296

includes 3 figures

arxiv created 2002/05/28 · arxiv updated 2009/11/30

Abstract

We prove a law of large numbers for a class of multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions, which hold when the environment is a weak mixing field in the sense of Dobrushin and Shlosman. Our result holds if the mixing rate balances moments of some random times depending on the path. It applies in the non-nestling case, but we also provide examples of nestling walks that satisfy our assumptions. The derivation is based on an adaptation, using coupling, of the regeneration argument of Sznitman-Zerner.

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