Mixing and hitting times for finite Markov chains

Details Mixing and hitting times for finite Markov chains Mixing and hitting times for finite Markov chains

2011-08-08

arxiv.org/abs/1108.1708v1

Mathematics

Probability

15 pages

Scientific paper

Let 0<\alpha<1/2. We show that the mixing time of a continuous-time reversible Markov chain on a finite state space is about as large as the largest expected hitting time of a subset of stationary measure at least \alpha of the state space. Suitably modified results hold in discrete time and/or without the reversibility assumption. The key technical tool is a construction of a random set A such that the hitting time of A is both light-tailed and a stationary time for the chain. We note that essentially the same results were obtained independently by Peres and Sousi [arXiv:1108.0133].

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