Recurrence of Simple Random Walk on Z 2 is Dynamically Sensitive
نویسنده
چکیده
Benjamini, Häggström, Peres and Steif [2] introduced the concept of a dynamical random walk. This is a continuous family of random walks, {Sn(t)}n∈N,t∈R. Benjamini et. al. proved that if d = 3 or d = 4 then there is an exceptional set of t such that {Sn(t)}n∈N returns to the origin infinitely often. In this paper we consider a dynamical random walk on Z2. We show that with probability one there exists t ∈ R such that {Sn(t)}n∈N never returns to the origin. This exceptional set of times has dimension one. This proves a conjecture of Benjamini et. al. [2].
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تاریخ انتشار 2008