The simple exclusion process on the circle has a diffusive cutoff window

In this paper, we investigate the mixing time of the simple exclusion process on the circle with N sites, with a number of particle k(N) tending to infinity, both from the worst initial condition and from a typical initial condition. We show that the worst-case mixing time is asymptotically equivalent to (8 pi(2))(-1) N-2 log k, while the cutoff window is identified to be N-2. Starting from a typical condition, we show that there is no cutoff and that the mixing time is of order N-2.