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February, 1991 Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process
James Allen Fill
Ann. Appl. Probab. 1(1): 62-87 (February, 1991). DOI: 10.1214/aoap/1177005981

Abstract

We extend recently developed eigenvalue bounds on mixing rates for reversible Markov chains to nonreversible chains. We then apply our results to show that the $d$-particle simple exclusion process corresponding to clockwise walk on the discrete circle $\mathbf{Z}_p$ is rapidly mixing when $d$ grows with $p$. The dense case $d = p/2$ arises in a Poisson blockers problem in statistical mechanics.

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James Allen Fill. "Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process." Ann. Appl. Probab. 1 (1) 62 - 87, February, 1991. https://doi.org/10.1214/aoap/1177005981

Information

Published: February, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0726.60069
MathSciNet: MR1097464
Digital Object Identifier: 10.1214/aoap/1177005981

Subjects:
Primary: 60J10
Secondary: 15A42 , 60J27 , 60K35

Keywords: Cheege's inequality , chi-square distance , Exclusion process , interacting particle systems , Markov chains , Poincare inequality , Poisson blockers , rapid mixing , rates of convergence , reversibility , variation distance

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.1 • No. 1 • February, 1991
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