Open Access
2009 Recurrence and transience of a multi-excited random walk on a regular tree
Anne-Laure Basdevant, Arvind Singh
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Electron. J. Probab. 14: 1628-1669 (2009). DOI: 10.1214/EJP.v14-672


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.


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Anne-Laure Basdevant. Arvind Singh. "Recurrence and transience of a multi-excited random walk on a regular tree." Electron. J. Probab. 14 1628 - 1669, 2009.


Accepted: 9 July 2009; Published: 2009
First available in Project Euclid: 1 June 2016

zbMATH: 1203.60143
MathSciNet: MR2525106
Digital Object Identifier: 10.1214/EJP.v14-672

Primary: 60F20
Secondary: 60J80 , 60K35

Keywords: branching Markov chain , Multi-excited random walk , Self-interacting random walk

Vol.14 • 2009
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