Cheeger inequalities for absorbing Markov chains. (September 2016)

• Record Type: Journal Article
• Authors: Froyland, Gary; Stuart, Robyn M.
• Is Part Of: Advances in applied probability. Volume 48:Number 3(2016)
• Page Start: 631
• Page End: 647
• Publication Date: 2016-09
• Subjects: Absorbing Markov chain, -- transient Markov chain, -- substochastic transition matrix, -- quasistationary distribution, -- Cheeger constant, -- conductance, -- metastability; Primary 60J10; Probabilities -- Periodicals; Stochastic models -- Periodicals; Electronic journals; Periodicals; 519.2
• DOI: 10.1017/apr.2016.20
• Languages: English
• ISSNs: 0001-8678

Abstract

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.