ONE-POINT ASYMPTOTICS FOR HALF-FLAT ASEP

• 成果类型: Article
• 署名作者: Dimitrov, Evgeni; Murthy, Anushka
• 署名单位: University of South Carolina System; University of South Carolina Columbia; Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1987
• 发表日期: 2024
• 页码: 1136-1176
• 关键词: kpz; GROWTH; tasep

摘要

We consider the asymmetric simple exclusion process (ASEP) with half-flat initial condition. We show that the one-point marginals of the ASEP height function are described by those of the Airy(2 -> 1) process, introduced by Borodin-Ferrari-Sasamoto in (Comm. Pure Appl. Math. 61 (2008) 1603-1629). This result was conjectured by Ortmann-Quastel-Remenik (Ann. Appl. Probab. 26 (2016) 507-548), based on an informal asymptotic analysis of exact formulas for generating functions of the half-flat ASEP height function at one spatial point. Our present work provides a fully rigorous derivation and asymptotic analysis of the same generating functions, under certain parameter restrictions of the model.