ASYMPTOTICS OF COVER TIMES VIA GAUSSIAN FREE FIELDS: BOUNDED-DEGREE GRAPHS AND GENERAL TREES

• 成果类型: Article
• 署名作者: Ding, Jian
• 署名单位: Stanford University; University of Chicago
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP822
• 发表日期: 2014
• 页码: 464-496
• 关键词: markov-processes; random-walks; brownian-motion

摘要

In this paper we show that on bounded degree graphs and general trees, the cover time of the simple random walk is asymptotically equal to the product of the number of edges and the square of the expected supremum of the Gaussian free field on the graph, assuming that the maximal hitting time is significantly smaller than the cover time. Previously, this was only proved for regular trees and the 2D lattice. Furthermore, for general trees, we derive exponential concentration for the cover time, which implies that the standard deviation of the cover time is bounded by the geometric mean of the cover time and the maximal hitting time.