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Mixing times for uniformly ergodic Markov chains

Author

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  • Aldous, David
  • Lovász, László
  • Winkler, Peter

Abstract

Consider the class of discrete time, general state space Markov chains which satisfy a "uniform ergodicity under sampling" condition. There are many ways to quantify the notion of "mixing time", i.e., time to approach stationarity from a worst initial state. We prove results asserting equivalence (up to universal constants) of different quantifications of mixing time. This work combines three areas of Markov theory which are rarely connected: the potential-theoretical characterization of optimal stopping times, the theory of stability and convergence to stationarity for general-state chains, and the theory surrounding mixing times for finite-state chains.

Suggested Citation

  • Aldous, David & Lovász, László & Winkler, Peter, 1997. "Mixing times for uniformly ergodic Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 71(2), pages 165-185, November.
    • Handle: RePEc:eee:spapps:v:71:y:1997:i:2:p:165-185
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    Cited by:

    1. Baudel, Manon & Guyader, Arnaud & Lelièvre, Tony, 2023. "On the Hill relation and the mean reaction time for metastable processes," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 393-436.
    2. Souissi, Abdessatar & Soueidy, El Gheteb & Barhoumi, Abdessatar, 2023. "On a ψ-Mixing property for Entangled Markov Chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).

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