Separation cut-offs for birth and death chains
Persi Diaconis and Laurent Saloff-Coste
Source: Ann. Appl. Probab. Volume 16, Number 4
(2006), 2098-2122.
Abstract
This paper gives a necessary and sufficient condition for a sequence of birth and death chains to converge abruptly to stationarity, that is, to present a cut-off. The condition involves the notions of spectral gap and mixing time. Y. Peres has observed that for many families of Markov chains, there is a cut-off if and only if the product of spectral gap and mixing time tends to infinity. We establish this for arbitrary birth and death chains in continuous time when the convergence is measured in separation and the chains all start at 0.
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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1169065218
Digital Object Identifier: doi:10.1214/105051606000000501
Mathematical Reviews number (MathSciNet): MR2288715
Zentralblatt MATH identifier: 1127.60081
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