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

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

2008-03-22

arxiv.org/abs/0803.3284v3

Mathematics

Probability

Major modifications. Simplified the proof of recurrence/transience and added a proof of recurrence in the critical case. Added

Scientific paper

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 of the recurrence/transience property of the walk. In particular, we prove that the asymptotic behavior 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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