Abstract
Abstract
We prove that for a sequence of finite vertex-transitive graphs of increasing sizes, the cover times are asymptotically concentrated if and only if the product of the spectral gap and the expected cover time diverges. In fact, we prove this for general reversible Markov chains under the much weaker assumption (than transitivity) that the maximal hitting time of a state is of the same order as the average hitting time.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference41 articles.
1. Aldous, D.: Hitting times for random walks on vertex-transitive graphs. Math. Proc. Camb. Philos. Soc. 106(1), 179–191 (1989)
2. Aldous, D.: Random walk covering of some special trees. J. Math. Anal. Appl. 157(1), 271–283 (1991)
3. Aldous, D.: Some inequalities for reversible Markov chains. J. Lond. Math. Soc. 2(3), 564–576 (1982)
4. Aldous, D.: Threshold limits for cover times. J. Theor. Probab. 4(1), 197–211 (1991)
5. Aldous, D., Fill, J.: Reversible Markov chains and random walks on graphs. Unfinished manuscript. Available at the first author’s
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