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Comparison of Cutoffs Between Lazy Walks and Markovian Semigroups

Part of: Markov processes

Published online by Cambridge University Press:  30 January 2018

Guan-Yu Chen  and
Laurent Saloff-Coste
Guan-Yu Chen*
Affiliation:
National Chiao Tung University
Laurent Saloff-Coste*
Affiliation:
Cornell University
*
∗ Postal address: Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan. Email address: gychen@math.nctu.edu.tw
∗∗ Postal address: Malott Hall, Department of Mathematics, Cornell University, Ithaca, NY 14853-4201. Email address: lsc@math.cornell.edu
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Abstract

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We make a connection between the continuous time and lazy discrete time Markov chains through the comparison of cutoffs and mixing time in total variation distance. For illustration, we consider finite birth and death chains and provide a criterion on cutoffs using eigenvalues of the transition matrix.

Keywords

Markov chaincutoff phenomenon

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 4 , December 2013 , pp. 943 - 959
Copyright
© Applied Probability Trust 

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