A special set of exceptional times for dynamical random walk on Z2
Gideon Amir, University of Toronto
Christopher Hoffman, University of Washington
Abstract
In [2] Benjamini, Haggstrom, Peres and Steif introduced the model of dynamical random walk on the d-dimensional lattice Z^d. This is a continuum of random walks indexed by a time parameter t. They proved that for dimensions d=3,4 there almost surely exist times t such that the random walk at time t visits the origin infinitely often, but for dimension 5 and up there almost surely do not exist such t. Hoffman showed that for dimension 2 there almost surely exists t such that the random walk at time t visits the origin only finitely many times [5]. We refine the results of [5] for dynamical random walk on Z^2, showing that with probability one the are times when the origin is visited only a finite number of times while other points are visited infinitely often.
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