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Recurrence of the $\mathbb{Z}^d$-valued infinite snake via unimodularity


 
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1. Title Title of document Recurrence of the $\mathbb{Z}^d$-valued infinite snake via unimodularity
 
2. Creator Author's name, affiliation, country Itai Benjamini; Weizmann Institute of Science; Israel
 
2. Creator Author's name, affiliation, country Nicolas Curien; École Normale Supérieure Paris; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Galton-Watson trees; random snake; recurrence
 
3. Subject Subject classification 60J80
 
4. Description Abstract We use the concept of unimodular random graph to show that the branching simple random walk on $\mathbb{Z}^{d}$ indexed by a critical geometric Galton-Watson tree conditioned to survive is recurrent if and only if $d \leq 4$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 2012-01-02
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1700
 
10. Identifier Digital Object Identifier 10.1214/ECP.v17-1700
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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