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

被引：5

作者：

Caravenna, Francesco ^{[1
]}

Sun, Rongfeng ^{[2
]}

Zygouras, Nikos ^{[3
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicazioni, Milan, Italy

[2] Natl Univ Singapore, Dept Math, Singapore, Singapore

[3] Univ Warwick, Dept Math, Warwick, England

来源：

ANNALS OF PROBABILITY | 2023年 / 51卷 / 06期

基金：

英国工程与自然科学研究理事会;

关键词：

Directed polymer in random environment; Gaussian multiplicative chaos; Gaussian; correlation inequality; stochastic heat equation; stochastic heat flow; KPZ equation; EQUATION; POLYMER;

D O I：

10.1214/23-AOP1648

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：2265 / 2300

页数：36

共 25 条

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ANDERSON T. W., 1955, P AM MATH SOC, V6, P170

[2] THE STOCHASTIC HEAT-EQUATION - FEYNMAN-KAC FORMULA AND INTERMITTENCE [J].