The Point of View of the Particle on the Law of Large Numbers for Random Walks in a Mixing Random Environment

Details 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

2002-06-17

arxiv.org/abs/math/0206160v3

Ann. Probab. 31, no. 3 (2003), 1441--1463

Mathematics

Probability

22 pages. To appear in the Annals of Probability

Scientific paper

10.1214/aop/1055425786

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.

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