The critical 2d Stochastic Heat Flow is not a Gaussian Multiplicative Chaos

Abstract

The critical $2d$ Stochastic Heat Flow (SHF) is a stochastic process of random measures on ${\mathbb{R}}^2$, recently constructed in [CSZ23]. We show that this process falls outside the class of Gaussian Multiplicative 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.

Final version. 38 pages, 5 figures

References in corpus (3)

• Moments of the 2d directed polymer in the subcritical regime and a generalisation of the Erdös-Taylor theorem
• The critical 2D delta-Bose gas as mixed-order asymptotics of planar Brownian motion
• Geometry of the Gaussian multiplicative chaos in the Wiener space

Cited by in corpus (3)

• The Allen-Cahn equation with weakly critical random initial datum
• Mesoscopic averaging of the two-dimensional KPZ equation
• Two dimensional delta Bose gas in a weighted space