Fill, James Allen, Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process, Annals of applied probability , 1(1), 1991, pp. 62-87
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 Zp is rapidly mixing when d grows with p. The dense case d=p/2 arises in a Poisson blockers problem in statistical mechanics.