The Annals of Probability

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

Francis Comets and Ofer Zeitouni

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Abstract

We prove a law of large numbers for a class of ballistic, 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 nonnestling 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 and Zerner.

Article information

Source
Ann. Probab., Volume 32, Number 1B (2004), 880-914.

Dates
First available in Project Euclid: 11 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.aop/1079021467

Digital Object Identifier
doi:10.1214/aop/1079021467

Mathematical Reviews number (MathSciNet)
MR2039946

Zentralblatt MATH identifier
1078.60089

Subjects
Primary: 60K40: Other physical applications of random processes 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

Keywords
Random walk in random environment law of large numbers Kalikow's condition nestling walk mixing

Citation

Comets, Francis; Zeitouni, Ofer. A law of large numbers for random walks in random mixing environments. Ann. Probab. 32 (2004), no. 1B, 880--914. doi:10.1214/aop/1079021467. https://projecteuclid.org/euclid.aop/1079021467


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