RESEARCH ARTICLE

Explicit criteria on separation cutoff for birth and death chains

  • Yonghua MAO ,
  • Yuhui ZHANG
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  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received date: 03 Mar 2014

Accepted date: 03 Apr 2014

Published date: 20 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

The criteria on separation cutoff for birth and death chains were obtained by Diaconis and Saloff-Coste in 2006. These criteria are involving all eigenvalues. In this paper, we obtain the explicit criterion, which depends only on the birth and death rates. Furthermore, we present two ways to estimate moments of the fastest strong stationary time and then give another but equivalent criterion explicitly.

Cite this article

Yonghua MAO , Yuhui ZHANG . Explicit criteria on separation cutoff for birth and death chains[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 881 -898 . DOI: 10.1007/s11464-014-0380-8

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