Phase transition for the Once-reinforced random walk on ℤ^d-like trees

2016/04/26 by Kious, Daniel, Sidoravicius, Vladas
#60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1604.07631

Abstract

In this short paper, we consider the Once-reinforced random walk with reinforcement parameter a on trees with bounded degree which are transient for the simple random walk. On each of these trees, we prove that there exists an explicit critical parameter a₀ such that the Once-reinforced random walk is almost surely recurrent if a>a₀ and almost surely transient if a

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