Electronic Journal of Probability

Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs

David Windisch

Full-text: Open access

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).

Article information

Source
Electron. J. Probab., Volume 15 (2010), paper no. 36, 1143-1160.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464819821

Digital Object Identifier
doi:10.1214/EJP.v15-787

Mathematical Reviews number (MathSciNet)
MR2659760

Zentralblatt MATH identifier
1226.60070

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60J05: Discrete-time Markov processes on general state spaces

Keywords
random walk range entropy

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Windisch, David. Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs. Electron. J. Probab. 15 (2010), paper no. 36, 1143--1160. doi:10.1214/EJP.v15-787. https://projecteuclid.org/euclid.ejp/1464819821


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References

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