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Critical Constants for Recurrence on Groups of Polynomial Growth


 
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1. Title Title of document Critical Constants for Recurrence on Groups of Polynomial Growth
 
2. Creator Author's name, affiliation, country David Revelle; Weizmann Institute of Science; Israel
 
2. Creator Author's name, affiliation, country Russ M Thompson; Cornell University; United States
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) nilpotent group; Schreier graph; random walk; recurrence; volume growth
 
3. Subject Subject classification 60B15; 20F65
 
4. Description Abstract The critical constant for recurrence, $c_{rt}$, is an invariant of the quotient space $H/G$ of a finitely generated group. The constant is determined by the largest moment a probability measure on $G$ can have without the induced random walk on $H/G$ being recurrent. We present a description of which subgroups of groups of polynomial volume growth are recurrent. Using this we show that for such recurrent subgroups $c_{rt}$ corresponds to the relative growth rate of $H$ in $G$, and in particular $c_{rt}$ is either $0$, $1$ or $2$.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) NSF Grants DMS-0603886 and EMSW21-RTG-0739164
 
7. Date (YYYY-MM-DD) 2010-04-16
 
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/773
 
10. Identifier Digital Object Identifier 10.1214/EJP.v15-773
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 15
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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