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October 1999 A Law of Large Numbers for Random Walks in Random Environment
Alain-Sol Sznitman, Martin Zerner
Ann. Probab. 27(4): 1851-1869 (October 1999). DOI: 10.1214/aop/1022874818


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.


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Alain-Sol Sznitman. Martin Zerner. "A Law of Large Numbers for Random Walks in Random Environment." Ann. Probab. 27 (4) 1851 - 1869, October 1999.


Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0965.60100
MathSciNet: MR1742891
Digital Object Identifier: 10.1214/aop/1022874818

Primary: 60K40
Secondary: 82D30

Keywords: Kalikow’s condition , Law of Large Numbers , Random walk in random environment , Renewal structure

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 4 • October 1999
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