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Recurrence and transience of a multi-excited random walk on a regular tree


 
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1. Title Title of document Recurrence and transience of a multi-excited random walk on a regular tree
 
2. Creator Author's name, affiliation, country Anne-Laure Basdevant; University Toulouse III
 
2. Creator Author's name, affiliation, country Arvind Singh; Zurich University
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Multi-excited random walk, self-interacting random walk, branching Markov chain
 
3. Subject Subject classification 60F20; 60K35; 60J80
 
4. Description Abstract We study a model of multi-excited random walk on a regular tree which generalizes the models of the once excited random walk and the digging random walk introduced by Volkov (2003). We show the existence of a phase transition and provide a criterion for the recurrence/transience property of the walk. In particular, we prove that the asymptotic behaviour of the walk depends on the order of the excitations, which contrasts with the one dimensional setting studied by Zerner (2005). We also consider the limiting speed of the walk in the transient regime and conjecture that it is not a monotonic function of the environment.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) Swiss Science Foundation, grant PDAM2-114536/1.
 
7. Date (YYYY-MM-DD) 2009-07-09
 
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/672
 
10. Identifier Digital Object Identifier 10.1214/EJP.v14-672
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 14
 
12. Language English=en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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