Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process. (English) Zbl 0726.60069

Fill, James Allen

Ann. Appl. Probab. 1, No. 1, 62-87 (1991).

The paper is closely connected with that of P. Diaconis and D. Stroock [ibid. 1, No.1, 36-61 (1991)]. Author’s summary describes the main lines of the considerations well: “We extend recently developed 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 \(Z_ p\) is rapidly mixing when d grows with p. The dense case \(d=p/2\) arises in a Poisson blockers problem in statistical mechanics.”

Reviewer: W.Schenk (Dresden)

MSC:

60J10	Markov chains (discrete-time Markov processes on discrete state spaces)
60J27	Continuous-time Markov processes on discrete state spaces
60K35	Interacting random processes; statistical mechanics type models; percolation theory
15A42	Inequalities involving eigenvalues and eigenvectors

Keywords:

variation distance; interacting particle systems; mixing rates for reversible Markov chains; nonreversible chains; simple exclusion process; Poisson blockers; statistical mechanics