Moments of the 2D SHE at criticality

Abstract

We study the stochastic heat equation in two spatial dimensions with a multiplicative white noise, as the limit of the equation driven by a noise that is mollified in space and white in time. As the mollification radius $\epsilon \to 0$, we tune the coupling constant near the critical point, and show that the single time correlation functions converge to a limit written in terms of an explicit non-trivial semigroup. Our approach consists of two steps. First we show the convergence of the resolvent of the (tuned) two-dimensional delta Bose gas, by adapting the framework of Dimock and Rajeev (2004) to our setup of spatial mollification. Then we match this to the Laplace transform of our semigroup.

arXiv comment30 pages, 3 figures. Updated to match the version to be published

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Cited by in corpus (10)

• A forward-backward SDE from the 2D nonlinear stochastic heat equation
• The critical 2d Stochastic Heat Flow is not a Gaussian Multiplicative Chaos
• Gaussian fluctuations of a nonlinear stochastic heat equation in dimension two
• From Short-Range to Contact Interactions in Two-dimensional Many-Body Quantum Systems
• Moments of the 2d directed polymer in the subcritical regime and a generalisation of the Erdös-Taylor theorem
• Gaussian Limits for Subcritical Chaos
• On the Weakness of Short-Range Interactions in Fermi Gases
• Mesoscopic averaging of the two-dimensional KPZ equation
• Equivalence of fluctuations of discretized SHE and KPZ equations in the subcritical weak disorder regime
• Two dimensional delta Bose gas in a weighted space