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On the Range of the Simple Random Walk Bridge on Groups


 
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1. Title Title of document On the Range of the Simple Random Walk Bridge on Groups
 
2. Creator Author's name, affiliation, country Itai Benjamini; Weizmann Institute of Science
 
2. Creator Author's name, affiliation, country Roey Izkovsky; Weizmann Institute of Science
 
2. Creator Author's name, affiliation, country Harry Kesten; Cornell University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) range of random walk;range of a bridge
 
3. Subject Subject classification Primary 60K35; Secondary
 
4. Description Abstract Let $G$ be a vertex transitive graph. A study of the range of simple random walk on $G$ and of its bridge is proposed. While it is expected that on a graph of polynomial growth the sizes of the range of the unrestricted random walk and of its bridge are the same in first order, this is not the case on some larger graphs such as regular trees. Of particular interest is the case when $G$ is the Cayley graph of a group. In this case we even study the range of a general symmetric (not necessarily simple) random walk on $G$. We hope that the few examples for which we calculate the first order behavior of the range here will help to discover some relation between the group structure and the behavior of the range. Further problems regarding bridges are presented.
 
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6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2007-05-01
 
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/408
 
10. Identifier Digital Object Identifier 10.1214/EJP.v12-408
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 12
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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