The cutoff phenomenon for Ehrenfest chains

Abstract

"We consider families of Ehrenfest chains and provide a simple criterion on the L-P-cutoff and the L-P-precutoff with specified initial states for 1 <= p < infinity. For the family with an L-P-cutoff, a cutoff time is described and a possible window is given. For the family without an L-P-precutoff, the exact order of the L-P-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. (C) 2012 Elsevier B.V. All rights reserved."