Separation cut-offs for birth and death chains

Preprint

14 February 2007

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0702411

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.

Keywords

BIRTH AND DEATH
SEPARATION CUT
MARKOV CHAINS
DEATH CHAINS
SPECTRAL GAP
MIXING TIME
CONVERGENCE
CUT OFFS

All Related Versions

Version 1, 2007-02-14, ArXiv
Published version: The Annals of Applied Probability, 16 (4).

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