Open Access
2006 Markov chain comparison
Martin Dyer, Leslie Ann Goldberg, Mark Jerrum, Russell Martin
Probab. Surveys 3: 89-111 (2006). DOI: 10.1214/154957806000000041


This is an expository paper, focussing on the following scenario. We have two Markov chains, $\mathcal{M}$ and $\mathcal{M'}$. By some means, we have obtained a bound on the mixing time of $\mathcal{M'}$. We wish to compare $\mathcal{M}$ with $\mathcal{M'}$ in order to derive a corresponding bound on the mixing time of $\mathcal{M}$. 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.


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Martin Dyer. Leslie Ann Goldberg. Mark Jerrum. Russell Martin. "Markov chain comparison." Probab. Surveys 3 89 - 111, 2006.


Published: 2006
First available in Project Euclid: 24 April 2006

zbMATH: 1189.60135
MathSciNet: MR2216963
Digital Object Identifier: 10.1214/154957806000000041

Primary: 60J10 , 68W20
Secondary: 60J27

Keywords: Comparison , Markov chains , mixing time

Rights: Copyright © 2006 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.3 • 2006
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