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2010 Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs
David Windisch
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Electron. J. Probab. 15: 1143-1160 (2010). DOI: 10.1214/EJP.v15-787

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 (preprint).

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David Windisch. "Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs." Electron. J. Probab. 15 1143 - 1160, 2010. https://doi.org/10.1214/EJP.v15-787

Information

Accepted: 7 July 2010; Published: 2010
First available in Project Euclid: 1 June 2016

zbMATH: 1226.60070
MathSciNet: MR2659760
Digital Object Identifier: 10.1214/EJP.v15-787

Subjects:
Primary: 60G50
Secondary: 60J05

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Vol.15 • 2010
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