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

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 $\sqrt{{\mathcal{C}}_n{2}^{-(n+1)}}-m_n$ converges in distribution as $n\to \infty$, where $m_n$ is an explicit constant, and identify the limit.