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arXiv · 1304.4346

On the mixing time and spectral gap for birth and death chains

Guan-Yu Chen·Laurent Saloff-Coste
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Abstract

For birth and death chains, we derive bounds on the spectral gap and mixing time in terms of birth and death rates. Together with the results of Ding et al. in 2010, this provides a criterion for the existence of a cutoff in terms of the birth and death rates. A variety of illustrative examples are treated.

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Guan-Yu Chen, Laurent Saloff-Coste. 2013-04-16. On the mixing time and spectral gap for birth and death chains. https://arxiv.org/abs/1304.4346

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