Limit Law For The Cover Time Of A Random Walk On A Binary Tree

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 the sequence of random variables root C-n(2-(n+1)) - m(n), where m(n) is an explicit constant, converges in distribution as n ->infinity, and identify the limit.