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Mixing Times are Hitting Times of Large Sets

Author

Listed:
  • Yuval Peres

    (Microsoft Research)

  • Perla Sousi

    (University of Cambridge)

Abstract

We consider irreducible reversible discrete time Markov chains on a finite state space. Mixing times and hitting times are fundamental parameters of the chain. We relate them by showing that the mixing time of the lazy chain is equivalent to the maximum over initial states $$x$$ x and large sets $$A$$ A of the hitting time of $$A$$ A starting from $$x$$ x . We also prove that the first time when averaging over two consecutive time steps is close to stationarity is equivalent to the mixing time of the lazy version of the chain.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jotpro:v:28:y:2015:i:2:d:10.1007_s10959-013-0497-9
    DOI: 10.1007/s10959-013-0497-9
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    Cited by:

    1. Kavita Ramanan & Aaron Smith, 2018. "Bounds on Lifting Continuous-State Markov Chains to Speed Up Mixing," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1647-1678, September.
    2. Jonathan Hermon, 2020. "A Spectral Characterization for Concentration of the Cover Time," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2167-2184, December.

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