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

Guan-Yu Chen; Laurent Saloff-Coste

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

Guan-Yu Chen, Laurent Saloff-Coste

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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 [15], 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.

Original language	American English
Pages (from-to)	293-321
Number of pages	29
Journal	ALEA-Latin American Journal of Probability and Mathematical Statistics
Volume	10
Issue number	1
State	Published - 16 Apr 2013

Keywords

Cutoff phenomenon
Birth and death chains

Cite this

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title = "On the mixing time and spectral gap for birth and death chains",

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 resultsof Ding et al. in [15], this provides a criterion for the existence of a cutoffin terms of the birth and death rates. A variety of illustrative examples aretreated.",

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AU - Saloff-Coste, Laurent

PY - 2013/4/16

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N2 - 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 resultsof Ding et al. in [15], this provides a criterion for the existence of a cutoffin terms of the birth and death rates. A variety of illustrative examples aretreated.

AB - 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 resultsof Ding et al. in [15], this provides a criterion for the existence of a cutoffin terms of the birth and death rates. A variety of illustrative examples aretreated.

KW - Cutoff phenomenon

KW - Birth and death chains

M3 - Article

VL - 10

SP - 293

EP - 321

JO - ALEA-Latin American Journal of Probability and Mathematical Statistics

JF - ALEA-Latin American Journal of Probability and Mathematical Statistics

IS - 1

ER -

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

Abstract

Keywords

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Cite this