Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process
Fill, James Allen
Ann. Appl. Probab., Tome 1 (1991) no. 4, p. 62-87 / Harvested from Project Euclid
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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.
Publié le : 1991-02-14
Classification:  Markov chains,  reversibility,  variation distance,  rates of convergence,  rapid mixing,  Poincare inequality,  Cheege's inequality,  chi-square distance,  interacting particle systems,  exclusion process,  Poisson blockers,  60J10,  60J27,  60K35,  15A42 
@article{1177005981,
     author = {Fill, James Allen},
     title = {Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process},
     journal = {Ann. Appl. Probab.},
     volume = {1},
     number = {4},
     year = {1991},
     pages = { 62-87},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177005981}
}

Fill, James Allen. Eigenvalue Bounds on Convergence to Stationarity for Nonreversible Markov Chains, with an Application to the Exclusion Process. Ann. Appl. Probab., Tome 1 (1991) no. 4, pp.  62-87. http://gdmltest.u-ga.fr/item/1177005981/