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 Electronic Journal of Probability > Vol. 14 (2009) > Paper 55 open journal systems 


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

Anne-Laure Basdevant, University Toulouse III
Arvind Singh, Zurich University


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.


Full text: PDF

Pages: 1628-1669

Published on: July 9, 2009
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Electronic Journal of Probability. ISSN: 1083-6489