THE TWO-DIMENSIONAL KPZ EQUATION IN THE ENTIRE SUBCRITICAL REGIME

• 成果类型: Article
• 署名作者: Caravenna, Francesco; Sun, Rongfeng; Zygouras, Nikos
• 署名单位: University of Milano-Bicocca; National University of Singapore; University of Warwick
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1383
• 发表日期: 2020
• 页码: 1086-1127
• 关键词: stochastic heat-equation; central-limit-theorem; UNIVERSALITY; Invariance

摘要

We consider the KPZ equation in space dimension 2 driven by spacetime white noise. We showed in previous work that if the noise is mollified in space on scale epsilon and its strength is scaled as (beta) over cap/root vertical bar log epsilon vertical bar, then a transition occurs with explicit critical point (beta) over cap (c) = root 2 pi. Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as epsilon down arrow 0, for sufficiently small (beta) over cap. We prove here that the limit exists in the entire subcritical regime (beta) over cap is an element of (0, (beta) over cap (c)) and we identify it as the solution of an additive stochastic heat equation, establishing so-called Edwards-Wilkinson fluctuations. The same result holds for the directed polymer model in random environment in space dimension 2.