Cutoff profile of ASEP on a segment
成果类型：
Article
署名作者：
Bufetov, Alexey; Nejjar, Peter
署名单位：
Leipzig University; University of Bonn; University of Bonn
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-021-01104-x
发表日期：
2022
页码：
229-253
关键词：
摘要：
This paper studies the mixing behavior of the Asymmetric Simple Exclusion Process (ASEP) on a segment of length N. Our main result is that for particle densities in (0, 1), the total-variation cutoff window of ASEP is N-1/3 and the cutoff profile is 1 - F-GUE, where F-GUE is the Tracy-Widom distribution function. This also gives a new proof of the cutoff itself, shown earlier by Labbe and Lacoin. Our proof combines coupling arguments, the result of Tracy-Widom about fluctuations of ASEP started from the step initial condition, and exact algebraic identities coming from interpreting the multi-species ASEP as a random walk on a Hecke algebra.