Heavy range of the randomly biased walk on Galton-Watson trees in the slow movement regime

2020/09/29 by Chen, Xinxin
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2009.13866

Abstract

We consider the randomly biased random walk on trees in the slow movement regime as in [HS16], whose potential is given by a branching random walk in the boundary case. We study the heavy range up to the n-th return to the root, i.e., the number of edges visited more than k_n times. For k_n=n^θ with θ∈(0,1), we obtain the convergence in probability of the rescaled heavy range, which improves one result of [AD20].

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