KPZ equation with a small noise, deep upper tail and limit shape

• 成果类型: Article
• 署名作者: Gaudreau Lamarre, Pierre Yves; Lin, Yier; Tsai, Li-Cheng
• 署名单位: University of Chicago; Utah System of Higher Education; University of Utah
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01185-2
• 发表日期: 2023
• 页码: 885-920
• 关键词: linear statistics; edge

摘要

In this paper, we consider the KPZ equation under the weak noise scaling. That is, we introduce a small parameter root epsilon in front of the noise and let epsilon -> 0. We prove that the one-point large deviation rate function has a 3/2 power law in the deep upper tail. Furthermore, by forcing the value of the KPZ equation at a point to be very large, we prove a limit shape of the solution of the KPZ equation as epsilon -> 0. This confirms the physics prediction in Hartmann et al. (Phys Rev Res 1(3):032043, 2019), Kolokolov and Korshunov (Phys Rev B 75(14):140201, 2007, Phys Rev E 80(3):031107, 2009), Kamenev et al. (Phys Rev E 94(3):032108, 2016), Le Doussal et al. (Phys Rev Lett 117(7):070403, 2016) and Meerson et al. (Phys Rev Lett 116(7):070601, 2016).