Multiscale analysis of exit distributions for random walks in random environments
成果类型：
Article
署名作者：
Bolthausen, Erwin; Zeitouni, Ofer
署名单位：
University of Minnesota System; University of Minnesota Twin Cities; University of Zurich; Technion Israel Institute of Technology; Technion Israel Institute of Technology
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-006-0032-3
发表日期：
2007
页码：
581-645
关键词：
摘要：
We present a multiscale analysis for the exit measures from large balls in Z(d), d >= 3, of random walks in certain i.i.d. random environments which are small perturbations of the fixed environment corresponding to simple random walk. Our main assumption is an isotropy assumption on the law of the environment, introduced by Bricmont and Kupiainen. Under this assumption, we prove that the exit measure of the random walk in a random environment from a large ball, approaches the exit measure of a simple random walk from the same ball, in the sense that the variational distance between smoothed versions of these measures converges to zero. We also prove the transience of the random walk in random environment. The analysis is based on propagating estimates on the variational distance between the exit measure of the random walk in random environment and that of simple random walk, in addition to estimates on the variational distance between smoothed versions of these quantities.
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