The Annals of Probability
- Ann. Probab.
- Volume 27, Number 4 (1999), 1851-1869.
A Law of Large Numbers for Random Walks in Random Environment
We derive a law of large numbers for a class of multidimensional random walks in random environment satisfying a condition which first appeared in the work of Kalikow. The approach is based on the existence of a renewal structure under an assumption of “transience in the direction $l$ .” This extends, to a multidimensional context, previous work of Kesten. Our results also enable proving the convergence of the law of the environment viewed from the particle toward a limiting distribution.
Ann. Probab., Volume 27, Number 4 (1999), 1851-1869.
First available in Project Euclid: 31 May 2002
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Sznitman, Alain-Sol; Zerner, Martin. A Law of Large Numbers for Random Walks in Random Environment. Ann. Probab. 27 (1999), no. 4, 1851--1869. doi:10.1214/aop/1022874818. https://projecteuclid.org/euclid.aop/1022874818