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


 
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1. Title Title of document Entropy of Random Walk Range on Uniformly Transient and on Uniformly Recurrent Graphs
 
2. Creator Author's name, affiliation, country David Windisch; The Weizmann Institute of Science; Israel
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) random walk, range, entropy
 
3. Subject Subject classification 60G50; 60J05
 
4. Description 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).
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2010-07-07
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/787
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-787
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
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