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.
Citation
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
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