Cyril Labbé

Mixing points on an interval

Consider N points on the unit interval. Resample each point at rate one uniformly in between its two nearest neighbours. The question is: how much time is needed to reach equilibrium (the uniform measure on the simplex) starting from the worst initial condition ? I will present results in collaboration with Pietro Caputo and Hubert Lacoin where we identified the asymptotic of the mixing times and showed a cutoff phenomenon for the distance to equilibrium.