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 Probability Surveys > Vol. 3 (2006) open journal systems 

Markov chain comparison

Martin Dyer, University of Leeds
Leslie Ann Goldberg, University of Warwick
Mark Jerrum, University of Edinburgh
Russell Martin, University of Liverpool

This is an expository paper, focussing on the following scenario. We have two Markov chains, M and M'. By some means, we have obtained a bound on the mixing time of M'. We wish to compare M with M' in order to derive a corresponding bound on the mixing time of M. We investigate the application of the comparison method of Diaconis and Saloff-Coste to this scenario, giving a number of theorems which characterize the applicability of the method. We focus particularly on the case in which the chains are not reversible. The purpose of the paper is to provide a catalogue of theorems which can be easily applied to bound mixing times.

AMS 2000 subject classifications: Primary 60J10, 68W20; secondary 60J27.

Keywords: Markov chains, mixing time, comparison.

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Dyer, Martin, Goldberg, Leslie Ann, Jerrum, Mark, Martin, Russell, Markov chain comparison, Probability Surveys, 3, (2006), 89-111 (electronic).


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Probability Surveys. ISSN: 1549-5787