Cutoff phenomenon for the (weakly) asymmetric simple exclusion process
We consider k particles on a segment of size N evolving according to the simple exclusion dynamics. According to the strength of the asymmetry of the jump rates, we identify the first order asymptotic (as N goes to infinity) of the mixing times of this Markov chain. This study lets appear two main regimes of asymmetry in which a cutoff phenomenon occurs: the distance to equilibrium falls abruptly from 1 to 0. This is based on joint works with Hubert Lacoin (IMPA).