Mathematics – Probability
Scientific paper
2004-10-14
Probability Surveys 2006, Vol. 3, No. 0, 89-111
Mathematics
Probability
Published at http://dx.doi.org/10.1214/154957806000000041 in the Probability Surveys (http://www.i-journals.org/ps/) by the In
Scientific paper
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.
Dyer Martin
Goldberg Leslie Ann
Jerrum Mark
Martin Russell
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