Mixing times for the TASEP in the maximal current phase

Abstract

We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a segment of size N with open boundaries. We focus on the maximal current phase and prove that the mixing time is of order ${\mathit{N}}^{3/2}$, up to logarithmic corrections. In the triple point, where the TASEP with open boundaries approaches the Uniform distribution on the state space, we show that the mixing time is precisely of order ${\mathit{N}}^{3/2}$. This is conjectured to be the correct order of the mixing time for a wide range of particle systems with maximal current. Our arguments rely on a connection to last passage percolation and recent results on moderate deviations of last passage times.