Phase transition for the once-excited random walk on general trees

2018/12/05 by Huynh, Cong Bang
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1812.02331

Abstract

The phase transition of M-digging random on a general tree was studied by Collevecchio, Huynh and Kious (2018). In this paper, we study particularly the critical M-digging random walk on a superperiodic tree that is proved to be recurrent. We keep using the techniques introduced by Collevecchio, Kious and Sidoravicius (2017) with the aim of investigating the phase transition of Once-excited random walk on general trees. In addition, we prove if \mathcal T is a tree whose branching number is larger than 1, any multi-excited random walk on T moving, after excitation, like a simple random walk is transient.

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