Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process
Open Access
- 1 February 1991
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Applied Probability
- Vol. 1 (1), 62-87
- https://doi.org/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.