Probability Surveys

Markov chain comparison

Martin Dyer, Leslie Ann Goldberg, Mark Jerrum, and Russell Martin

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Abstract

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.

Article information

Source
Probab. Surveys, Volume 3 (2006), 89-111.

Dates
First available in Project Euclid: 24 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.ps/1145890796

Digital Object Identifier
doi:10.1214/154957806000000041

Mathematical Reviews number (MathSciNet)
MR2216963

Zentralblatt MATH identifier
1189.60135

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 68W20: Randomized algorithms
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces

Keywords
Markov chains mixing time comparison

Citation

Dyer, Martin; Goldberg, Leslie Ann; Jerrum, Mark; Martin, Russell. Markov chain comparison. Probab. Surveys 3 (2006), 89--111. doi:10.1214/154957806000000041. https://projecteuclid.org/euclid.ps/1145890796


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