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2012 Mixing and hitting times for finite Markov chains
Roberto Oliveira
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Electron. J. Probab. 17: 1-12 (2012). DOI: 10.1214/EJP.v17-2274

Abstract

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

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Roberto Oliveira. "Mixing and hitting times for finite Markov chains." Electron. J. Probab. 17 1 - 12, 2012. https://doi.org/10.1214/EJP.v17-2274

Information

Accepted: 27 August 2012; Published: 2012
First available in Project Euclid: 4 June 2016

zbMATH: 1251.60059
MathSciNet: MR2968677
Digital Object Identifier: 10.1214/EJP.v17-2274

Subjects:
Primary: 60J10

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