Résumé en anglais

In this paper, we investigate the mixing time of the simple exclusion processon the circle withNsites, with a number of particlek(N) tending to infinity. Fork6N/2We show that the mixing time is asymptotically equivalent to(8π2)−1N2logk, while thecutoff window which the time need for the distance to equilibrium to drop from 1−εtoεforε >0 is identified to beN2. We also prove that for most initial conditions, atimeO(N2) is sufficient for mixing. Some portion of the proof remains valid in higherdimension.