## The Annals of Probability

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

#### 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

#### 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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