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Cheeger inequalities for absorbing Markov chains

Part of: Markov processes

Published online by Cambridge University Press:  19 September 2016

Gary Froyland  and
Robyn M. Stuart
Gary Froyland*
Affiliation:
University of New South Wales
Robyn M. Stuart*
Affiliation:
University of New South Wales
*
* Postal address: School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia. Email address: [email protected]
** Current address: Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark.
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Abstract

We construct Cheeger-type bounds for the second eigenvalue of a substochastic transition probability matrix in terms of the Markov chain's conductance and metastability (and vice versa) with respect to its quasistationary distribution, extending classical results for stochastic transition matrices.

Keywords

Absorbing Markov chaintransient Markov chainsubstochastic transition matrixquasistationary distributionCheeger constantconductancemetastability

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 3 , September 2016 , pp. 631 - 647
Copyright
Copyright © Applied Probability Trust 2016 

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