BROWNIAN ABSOLUTE CONTINUITY OF THE KPZ FIXED POINT WITH ARBITRARY INITIAL CONDITION

• 成果类型: Article
• 署名作者: Sarkar, Sourav; Virag, Balint
• 署名单位: University of Toronto; University of Toronto
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/20-AOP1491
• 发表日期: 2021
• 页码: 1718-1737
• 关键词: airy; fluctuations

摘要

We show that the law of the KPZ fixed point starting from arbitrary initial condition is absolutely continuous with respect to the law of Brownian motion B on every compact interval. In particular, the Airy(1) process is absolutely continuous with respect to B on any compact interval.