The cutoff phenomenon for Ehrenfest chains

Guan-Yu Chen*, Yang Jen Fang, Yuan-Chung Sheu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider families of Ehrenfest chains and provide a simple criterion on the Lp-cutoff and the Lp-precutoff with specified initial states for 1≤p<∞. For the family with an Lp-cutoff, a cutoff time is described and a possible window is given. For the family without an Lp-precutoff, the exact order of the Lp-mixing time is determined. The result is consistent with the well-known conjecture on cutoffs of Markov chains proposed by Peres in 2004, which says that a cutoff exists if and only if the multiplication of the spectral gap and the mixing time tends to infinity.

Original languageEnglish
Pages (from-to)2830-2853
Number of pages24
JournalStochastic Processes and their Applications
Volume122
Issue number8
DOIs
StatePublished - 1 Aug 2012

Keywords

  • Cutoff phenomenon
  • Ehrenfest chains

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