The cutoff phenomenon for Ehrenfest chains

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 < ∞ . 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.