The point of view of the particle on the law of large numbers for random walks in a mixing random environment

The point of view of the particle on the law of large numbers for random walks in a mixing random environment

Firas Rassoul-Agha

Source: Ann. Probab. Volume 31, Number 3 (2003), 1441-1463.

Abstract

The point of view of the particle is an approach that has proven very powerful in the study of many models of random motions in random media. We provide a new use of this approach to prove the law of large numbers in the case of one or higher-dimensional, finite range, transient random walks in mixing random environments. One of the advantages of this method over what has been used so far is that it is not restricted to i.i.d. environments.

Primary Subjects: 60K40

Secondary Subjects: 82D30

Keywords: Random walks; random environments; point of view of the particle; law of large numbers; Kalikow's condition; Dobrushin--Shlosman mixing.

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1055425786
Digital Object Identifier: doi:10.1214/aop/1055425786
Mathematical Reviews number (MathSciNet): MR1989439
Zentralblatt MATH identifier: 02072326

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COLUMBUS, OHIO 43210-1174 E-MAIL: firas@math.ohio-state.edu URL: www.math.ny u.edu/ rassoul

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