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Markov chain mixing time on cycles


  • Balázs, Gerencsér


Mixing time quantifies the convergence speed of a Markov chain to the stationary distribution. It is an important quantity related to the performance of MCMC sampling. It is known that the mixing time of a reversible chain can be significantly improved by lifting, resulting in an irreversible chain, while changing the topology of the chain. We supplement this result by showing that if the connectivity graph of a Markov chain is a cycle, then there is an Ω ( n 2 ) lower bound for the mixing time. This is the same order of magnitude that is known for reversible chains on the cycle.

Suggested Citation

  • Balázs, Gerencsér, 2011. "Markov chain mixing time on cycles," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2553-2570, November.
  • Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2553-2570

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    References listed on IDEAS

    1. Burdzy, Krzysztof & Kang, Weining & Ramanan, Kavita, 2009. "The Skorokhod problem in a time-dependent interval," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 428-452, February.
    2. Ren, Yao-Feng & Tian, Fan-Ji, 2003. "On the Rosenthal's inequality for locally square integrable martingales," Stochastic Processes and their Applications, Elsevier, vol. 104(1), pages 107-116, March.
    3. O. Garnet & A. Mandelbaum & M. Reiman, 2002. "Designing a Call Center with Impatient Customers," Manufacturing & Service Operations Management, INFORMS, vol. 4(3), pages 208-227, October.
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