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.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 DOI:
 10.48550/arXiv.1906.07276
 arXiv:
 arXiv:1906.07276
 Bibcode:
 2019arXiv190607276D
 Keywords:

 Mathematics  Probability