Mixing times for the TASEP on the circle

• 成果类型: Article
• 署名作者: Schmid, Dominik; Sly, Allan
• 署名单位: University of Augsburg; Princeton University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01466-0
• 发表日期: 2026-04
• 页码: 1161-1233
• 关键词: Totally asymmetric simple exclusion process; mixing times; last passage percolation; Flat geodesics; KPZ universality class; Second class particles; simple exclusion process; last-passage percolation; current fluctuations; cutoff; Coalescence; COMPETITION; geodesics; particle; BEHAVIOR; profile

摘要

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.