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Mixing times for the TASEP on the circle
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DOI：10.1007/s00440-026-01466-0.png)
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Abstract
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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 N2min(k,N-k)-1/2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N<^>{2}\min (k,N-k)<^>{-1/2}$$\end{document}, 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 universality 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.
Keywords:
Totally asymmetric simple exclusion process
Mixing times
Last passage percolation
Flat geodesics
KPZ universality class
Second class particles
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