Recurrence of Simple Random Walk on $Z^2$ is Dynamically Sensitive

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dc.creatorHoffman, Christopher
dc.date2005-03-03
dc.date.accessioned2026-07-07T05:17:39Z
dc.date.available2026-07-07T05:17:39Z
dc.descriptionBenjamini, 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.
dc.identifierhttps://arxiv.org/abs/math/0503065
dc.identifierhttp://arxiv.org/abs/math/0503065
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74380
dc.subjectProbability
dc.titleRecurrence of Simple Random Walk on $Z^2$ is Dynamically Sensitive
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