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

Published 16 Apr 2013 in math.PR | (1304.4346v1)

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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