Mixing Times are Hitting Times of Large Sets

Yuval Peres () and Perla Sousi ()
Additional contact information
Yuval Peres: Microsoft Research
Perla Sousi: University of Cambridge

Journal of Theoretical Probability, 2015, vol. 28, issue 2, 488-519

Abstract: 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.

Keywords: Markov chain; Mixing time; Hitting time; Stopping time; 60J10 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-013-0497-9

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