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Some universal estimates for reversible Markov chains

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1.	Title	Title of document	Some universal estimates for reversible Markov chains
2.	Creator	Author's name, affiliation, country	Mykhaylo Shkolnikov; University of California, Berkeley; United States
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Reversible Markov chains; convergence to equilibrium; time of coupling; entropy
3.	Subject	Subject classification	60J10; 94A17
4.	Description	Abstract	We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the $L^2$ norms. The estimates in total variation norm are obtained using a novel identity relating the convergence to equilibrium of a reversible Markov chain to the increase in the entropy of its one-dimensional distributions. In addition, we propose a universal way of defining the ultrametric partition structure on the state space of such Markov chains. Finally, for chains reversible with respect to the uniform measure, we show how the global convergence to equilibrium can be controlled using the entropy accumulated by the chain.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)	NSF grant DMS-08-06211
7.	Date	(YYYY-MM-DD)	2013-01-17
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/1749
10.	Identifier	Digital Object Identifier	10.1214/EJP.v18-1749
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 18
12.	Language	English=en	en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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