The critical 2d Stochastic Heat Flow

• 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: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01184-7
• 发表日期: 2023
• 页码: 325-460
• 关键词: directed polymers; kpz equation; path localization; random environment; partition-function; Scaling Limit; fluctuations; systems; UNIVERSALITY; dimensions

摘要

We consider directed polymers in random environment in the critical dimension d = 2, focusing on the intermediate disorder regime when the model undergoes a phase transition. We prove that, at criticality, the diffu-sively rescaled random field of partition functions has a unique scaling limit: a universal process of random measures on R-2 with logarithmic correlations, which we call the Critical 2d Stochastic Heat Flow. It is the natural candidate for the long sought solution of the critical 2d Stochastic Heat Equation with multiplicative space-time white noise.