A sharp estimate for cover times on binary trees

Details A sharp estimate for cover times on binary trees A sharp estimate for cover times on binary trees

2011-04-03

arxiv.org/abs/1104.0434v1

Mathematics

Probability

14 pages, no figure

Scientific paper

We compute the second order correction for the cover time of the binary tree of depth $n$ by (continuous-time) random walk, and show that with probability approaching 1 as $n$ increases, $\sqrt{\tau_{\mathrm{cov}}}=\sqrt{|E|}[\sqrt{2\log 2}\cdot n - {\log n}/{\sqrt{2\log 2}} + O((\log\logn)^8]$, thus showing that the second order correction differs from the corresponding one for the maximum of the Gaussian free field on the tree.

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