Advances in Applied Probability

Cheeger inequalities for absorbing Markov chains

Gary Froyland and Robyn M. Stuart

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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.

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

First available in Project Euclid: 19 September 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Froyland, Gary; Stuart, Robyn M. Cheeger inequalities for absorbing Markov chains. Adv. in Appl. Probab. 48 (2016), no. 3, 631--647.

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