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

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

2002-05-28

arxiv.org/abs/math/0205296v1

Mathematics

Probability

includes 3 figures

Scientific paper

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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