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A Spectral Characterization for Concentration of the Cover Time

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  • Jonathan Hermon

    (University of Cambridge)

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.

Suggested Citation

  • Jonathan Hermon, 2020. "A Spectral Characterization for Concentration of the Cover Time," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2167-2184, December.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:4:d:10.1007_s10959-019-00946-5
    DOI: 10.1007/s10959-019-00946-5
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    References listed on IDEAS

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    1. Ding, Jian & Zeitouni, Ofer, 2012. "A sharp estimate for cover times on binary trees," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2117-2133.
    2. Yuval Peres & Perla Sousi, 2015. "Mixing Times are Hitting Times of Large Sets," Journal of Theoretical Probability, Springer, vol. 28(2), pages 488-519, June.
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