Advances in Applied Probability

Cheeger inequalities for absorbing Markov chains

Gary Froyland and Robyn M. Stuart

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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.

Article information

Source
Adv. in Appl. Probab., Volume 48, Number 3 (2016), 631-647.

Dates
First available in Project Euclid: 19 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.aap/1474296307

Mathematical Reviews number (MathSciNet)
MR3568884

Zentralblatt MATH identifier
1351.60091

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Absorbing Markov chain transient Markov chain substochastic transition matrix quasistationary distribution Cheeger constant conductance metastability

Citation

Froyland, Gary; Stuart, Robyn M. Cheeger inequalities for absorbing Markov chains. Adv. in Appl. Probab. 48 (2016), no. 3, 631--647. https://projecteuclid.org/euclid.aap/1474296307


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