Mixing times for the TASEP on the circle

TL;DR

This paper determines the mixing times for the TASEP on a circle, revealing a specific order and confirming the absence of cutoff, using connections to last passage percolation and novel analytical techniques.

Contribution

It provides the first precise order of mixing times for TASEP on a circle and introduces new methods linking TASEP to last passage percolation.

Findings

Mixing time is of order N^2 / sqrt(k(N-k))

Cutoff phenomenon does not occur in this setting

Analysis confirms predictions for KPZ universality class

Abstract

We study mixing times for the totally asymmetric simple exclusion process (TASEP) on a circle of length $N$ with $k$ particles. We show that the mixing time is of order $N^2 \min(k,N-k)^{-1/2}$, and that the cutoff phenomenon does not occur. This confirms behavior which was separately predicted by Jara, Lacoin and Peres, and it is more broadly believed to hold for integrable models in the KPZ-universalty class. Our arguments rely on a connection to periodic last passage percolation with a detailed analysis of flat geodesics, as well as a novel random extension and time shift argument for last passage percolation.