## The Annals of Applied Probability

### Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process

James Allen Fill

#### 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.

#### Article information

Source
Ann. Appl. Probab. Volume 1, Number 1 (1991), 62-87.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aoap/1177005981

Digital Object Identifier
doi:10.1214/aoap/1177005981

Mathematical Reviews number (MathSciNet)
MR1097464

Zentralblatt MATH identifier
0726.60069

JSTOR