The Annals of Probability

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

Firas Rassoul-Agha

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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.

Article information

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

Dates
First available in Project Euclid: 12 June 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1055425786

Digital Object Identifier
doi:10.1214/aop/1055425786

Mathematical Reviews number (MathSciNet)
MR1989439

Zentralblatt MATH identifier
1039.60089

Subjects
Primary: 60K40: Other physical applications of random processes
Secondary: 82D30: Random media, disordered materials (including liquid crystals and spin glasses)

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

Citation

Rassoul-Agha, Firas. The point of view of the particle on the law of large numbers for random walks in a mixing random environment. Ann. Probab. 31 (2003), no. 3, 1441--1463. doi:10.1214/aop/1055425786. https://projecteuclid.org/euclid.aop/1055425786


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