A Law of Large Numbers for Random Walks in Random
Environment
Alain-Sol Sznitman and Martin Zerner
Source: Ann. Probab.
Volume 27, Number 4
(1999), 1851-1869.
Abstract
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.
Primary Subjects: 60K40
Secondary Subjects: 82D30
Keywords: Random walk in random environment; law of large numbers; Kalikow’s condition; renewal structure
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aop/1022874818
Mathematical Reviews number (MathSciNet):
MR1742891
Digital Object Identifier: doi:10.1214/aop/1022874818
Zentralblatt MATH identifier:
0965.60100
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