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Almost Sure Recurrence of the Simple Random Walk Path

Itai Benjamini·Ori Gurel-Gurevich
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Abstract

It is shown that the path of a simple random walk on any graph, consisting of all vertices visited and edges crossed by the walk, is almost surely a recurrent subgraph.

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Itai Benjamini, Ori Gurel-Gurevich. 2008-08-04. Almost Sure Recurrence of the Simple Random Walk Path. https://arxiv.org/abs/math/0508270

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