Limit law for the cover time of a random walk on a binary tree

2019/06/17 by Dembo, Amir, Rosen, Jay, Zeitouni, Ofer · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1906.07276

Abstract

Let T_n denote the binary tree of depth n augmented by an extra edge connected to its root. Let C_n denote the cover time of T_n by simple random walk. We prove that √ C_n 2^-(n+1) - m_n converges in distribution as n→ ∞, where m_n is an explicit constant, and identify the limit.

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• Tail distributions of cover times of once-reinforced random walks

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