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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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

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

First available in Project Euclid: 11 March 2004

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Zentralblatt MATH identifier

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

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


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.

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