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