Vol. 2, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 1
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 2690-1005
ISSN (print): 2690-0998
Author Index
To Appear
 
Other MSP Journals
Moments of the 2D SHE at criticality

Yu Gu, Jeremy Quastel and Li-Cheng Tsai

Vol. 2 (2021), No. 1, 179–219
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 𝜀 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 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.

Keywords
stochastic heat equation, delta Bose gas, two-dimensional, critical
Mathematical Subject Classification
Primary: 60H15
Secondary: 35R60, 82D60, 46N30
Milestones
Received: 5 April 2020
Revised: 22 September 2020
Accepted: 11 October 2020
Published: 16 March 2021
Authors
Yu Gu
Department of Mathematics
Carnegie Mellon University
Pittsburgh PA
United States
Jeremy Quastel
Department of Mathematics
University of Toronto
Toronto ON
Canada
Li-Cheng Tsai
Department of Mathematics
Rutgers University
New Brunswick
Piscataway NJ
United States