MIXING TIMES FOR THE SIMPLE EXCLUSION PROCESS WITH OPEN BOUNDARIES

• 成果类型: Article
• 署名作者: Gantert, Nina; Nestoridi, Evita; Schmid, Dominik
• 署名单位: Technical University of Munich; Princeton University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1839
• 发表日期: 2023
• 页码: 972-1012
• 关键词: shock fluctuations; cutoff; profile; asep

摘要

We study mixing times of the symmetric and asymmetric simple exclu-sion process on the segment where particles are allowed to enter and exit at the endpoints. We consider different regimes depending on the entering and exiting rates as well as on the rates in the bulk, and show that the pro-cess exhibits pre-cutoff and in some cases cutoff. Our main contribution is to study mixing times for the asymmetric simple exclusion process with open boundaries. We show that the order of the mixing time can be linear or ex-ponential in the size of the segment depending on the choice of the boundary parameters, proving a strikingly different (and richer) behavior for the simple exclusion process with open boundaries than for the process on the closed segment. Our arguments combine coupling, second class particle and censor-ing techniques with current estimates. A novel idea is the use of multi-species particle arguments, where the particles only obey a partial ordering.