Separation cutoffs for birth death chains (2006)
by
Persi Diaconis
,
Laurent Saloff-Coste
| Citations: | 8 - 2 self |
BibTeX
@MISC{Diaconis06separationcutoffs,
author = {Persi Diaconis and Laurent Saloff-Coste},
title = {Separation cutoffs for birth death chains},
year = {2006}
}
OpenURL
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 cutoff 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.







