Fill, James Allen Eigenvalue bounds on convergence to stationarity for nonreversible Markov chains, with an application to the exclusion process. (English) Zbl 0726.60069 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) Cited in 5 ReviewsCited in 80 Documents 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 PDF BibTeX XML Cite \textit{J. A. Fill}, Ann. Appl. Probab. 1, No. 1, 62--87 (1991; Zbl 0726.60069) Full Text: DOI OpenURL