%0 Journal Article
%T A special set of exceptional times for dynamical random walk on $\Z^2$
%A Gideon Amir
%A Christopher Hoffman
%J Mathematics
%D 2006
%I arXiv
%X Benjamini,Haggstrom, Peres and Steif introduced the model of dynamical random walk on Z^d. This is a continuum of random walks indexed by a parameter t. They proved that for d=3,4 there almost surely exist t such that the random walk at time t visits the origin infinitely often, but for d > 4 there almost surely do not exist such t. Hoffman showed that for d=2 there almost surely exists t such that the random walk at time t visits the origin only finitely many times. We refine the results of Hoffman for dynamical random walk on Z^2, showing that with probability one there are times when the origin is visited only a finite number of times while other points are visited infinitely often.
%U http://arxiv.org/abs/math/0609267v2