Entropy of random walk range on uniformly transient and on uniformly recurrent graphs
David Windisch, The Weizmann Institute of Science
Abstract
We study the entropy of the distribution of the set Rn 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 Rn 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 (preprint).
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