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January 2004 A law of large numbers for random walks in random mixing environments
Francis Comets, Ofer Zeitouni
Ann. Probab. 32(1B): 880-914 (January 2004). DOI: 10.1214/aop/1079021467


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.


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Francis Comets. Ofer Zeitouni. "A law of large numbers for random walks in random mixing environments." Ann. Probab. 32 (1B) 880 - 914, January 2004.


Published: January 2004
First available in Project Euclid: 11 March 2004

zbMATH: 1078.60089
MathSciNet: MR2039946
Digital Object Identifier: 10.1214/aop/1079021467

Primary: 60K40 , 82D30

Keywords: Kalikow's condition , Law of Large Numbers , Mixing , nestling walk , Random walk in random environment

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 1B • January 2004
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