THE CRITICAL 2D STOCHASTIC HEAT FLOW IS NOT A GAUSSIAN MULTIPLICATIVE CHAOS

• 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: 10.1214/23-AOP1648
• 发表日期: 2023
• 页码: 2265-2300
• 关键词: equation; polymer

摘要

The critical 2d stochastic heat flow (SHF) is a stochastic process of ran-dom measures on R2, recently constructed in (Invent. Math. 233 (2023) 325- 460). We show that this process falls outside the class of Gaussian multiplica-tive chaos (GMC), in the sense that it cannot be realised as the exponential of a (generalised) Gaussian field. We achieve this by deriving strict lower bounds on the moments of the SHF that are of independent interest.