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 language | English |
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Pages (from-to) | 2830-2853 |
Number of pages | 24 |
Journal | Stochastic Processes and their Applications |
Volume | 122 |
Issue number | 8 |
DOIs | |
State | Published - 1 Aug 2012 |
Keywords
- Cutoff phenomenon
- Ehrenfest chains