# Moments of the 2D SHE at criticality

@article{Gu2019MomentsOT,
title={Moments of the 2D SHE at criticality},
author={Yu Gu and Jeremy Quastel and Li-Cheng Tsai},
journal={Probability and Mathematical Physics},
year={2019}
}
• Published 27 May 2019
• Mathematics
• Probability and Mathematical Physics
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 $\varepsilon\to 0$, 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…

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