A sharp estimate for cover times on binary trees

作者：Ding Jian^*; Zeitouni Ofer

来源：Stochastic Processes and Their Applications, 2012, 122(5): 2117-2133.

DOI：10.1016/j.spa.2012.03.008

• Cover time
• Random walk
• Gaussian free field

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,root tau(cov)=root vertical bar E parallel to root 2log 2n - log n / root 2 log 2 + O((log log n)(8))vertical bar, thus showing that the second order correction differs from the corresponding one for the maximum of the Gaussian free field on the tree.

• 出版日期2012-5