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Moments of the 2D SHE at
criticality
Yu Gu, Jeremy Quastel and Li-Cheng Tsai |
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Vol. 2 (2021), No. 1, 179–219
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Abstract |
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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 , 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 nontrivial 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 (J. Phys. A 37:39 (2004), 9157–9173) to our setup of spatial mollification. Then we match this to the Laplace transform of our semigroup. |
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Keywords
stochastic heat equation, delta Bose gas, two-dimensional,
critical
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Mathematical Subject Classification
Primary: 60H15
Secondary: 35R60, 82D60, 46N30
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Milestones
Received: 5 April 2020
Revised: 22 September 2020
Accepted: 11 October 2020
Published: 16 March 2021
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Authors |
| Yu Gu | |
| Department of Mathematics Carnegie Mellon University Pittsburgh PA United States |
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| Jeremy Quastel | |
| Department of Mathematics University of Toronto Toronto ON Canada |
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| Li-Cheng Tsai | |
| Department of Mathematics Rutgers University New Brunswick Piscataway NJ United States |
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