GUE x GUE LIMIT LAW AT HARD SHOCKS IN ASEP

• 成果类型: Article
• 署名作者: Nejjar, Peter
• 署名单位: University of Bonn
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1591
• 发表日期: 2021
• 页码: 321-350
• 关键词: markov-processes; fluctuations; tasep; particle

摘要

We consider the asymmetric simple exclusion process (ASEP) on Z with initial data such that in the large time particle density rho(.) a discontinuity (shock) at the origin is created. At the shock, the value of rho jumps from zero to one, but rho(-epsilon), 1 - rho(epsilon) > 0 for any epsilon > 0. We are interested in the rescaled position of a tagged particle which enters the shock with positive probability. We show that, inside the shock region, the particle position has the KPZ-typical 1/3 fluctuations, a F-GUE x F-GUE limit law and a degenerated correlation length. Outside the shock region, the particle fluctuates as if there was no shock. Our arguments are mostly probabilistic, in particular, the mixing times of countable state space ASEPs are instrumental to study the fluctuations at shocks.