Entropy of random walk range on uniformly transient and on uniformly recurrent graphs

David Windisch

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arXiv · 1001.0355

Entropy of random walk range on uniformly transient and on uniformly recurrent graphs

David Windisch

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Abstract

We study the entropy of the distribution of the set R_n of vertices visited by a simple random walk on a graph with bounded degrees in its first n steps. It is shown that this quantity grows linearly in the expected size of R_n if the graph is uniformly transient, and sublinearly in the expected size if the graph is uniformly recurrent with subexponential volume growth. This in particular answers a question asked by Benjamini, Kozma, Yadin and Yehudayoff (arXiv:0903.3179v1).

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David Windisch. 2010-07-11. Entropy of random walk range on uniformly transient and on uniformly recurrent graphs. https://arxiv.org/abs/1001.0355

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