A weakness in strong localization for Sinai's walk
成果类型：
Article
署名作者：
Shi, Zhan; Zindy, Olivier
署名单位：
Sorbonne Universite; Universite Paris Cite
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/009117906000000863
发表日期：
2007
页码：
1118-1140
关键词：
摘要：
Sinai's walk is a recurrent one-dimensional nearest-neighbor random walk in random environment. It is known for a phenomenon of strong localization, namely, the walk spends almost all time at or near the bottom of deep valleys of the potential. Our main result shows a weakness of this localization phenomenon: with probability one, the zones where the walk stays for the most time can be far away from the sites where the walk spends the most time. In particular, this gives a negative answer to a problem of Erdos and Revesz [Mathematical Structures-Computational Mathematics-Mathematical Modelling 2 (1984) 152-157], originally formulated for the usual homogeneous random walk.