Recurrence of Simple Random Walk on $Z^2$ is Dynamically Sensitive
概率论
2007-05-23 v1
摘要
Benjamini, Haggstrom, Peres and Steif introduced the concept of a dynamical random walk. This is a continuous family of random walks, {S_n(t)}. Benjamini et. al. proved that if d=3 or d=4 then there is an exceptional set of t such that {S_n(t)} returns to the origin infinitely often. In this paper we consider a dynamical random walk on Z^2. We show that with probability one there exists t such that {S_n(t)} never returns to the origin. This exceptional set of times has dimension one. This proves a conjecture of Benjamini et. al.
引用
@article{arxiv.math/0503065,
title = {Recurrence of Simple Random Walk on $Z^2$ is Dynamically Sensitive},
author = {Christopher Hoffman},
journal= {arXiv preprint arXiv:math/0503065},
year = {2007}
}