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May 2020 The two-dimensional KPZ equation in the entire subcritical regime
Francesco Caravenna, Rongfeng Sun, Nikos Zygouras
Ann. Probab. 48(3): 1086-1127 (May 2020). DOI: 10.1214/19-AOP1383

Abstract

We consider the KPZ equation in space dimension $2$ driven by space-time white noise. We showed in previous work that if the noise is mollified in space on scale $\varepsilon $ and its strength is scaled as $\hat{\beta }/\sqrt{|\log \varepsilon |}$, then a transition occurs with explicit critical point $\hat{\beta }_{c}=\sqrt{2\pi }$. Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as $\varepsilon \downarrow 0$, for sufficiently small $\hat{\beta }$. We prove here that the limit exists in the entire subcritical regime $\hat{\beta }\in (0,\hat{\beta }_{c})$ and we identify it as the solution of an additive stochastic heat equation, establishing so-called Edwards–Wilkinson fluctuations. The same result holds for the directed polymer model in random environment in space dimension $2$.

Citation

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Francesco Caravenna. Rongfeng Sun. Nikos Zygouras. "The two-dimensional KPZ equation in the entire subcritical regime." Ann. Probab. 48 (3) 1086 - 1127, May 2020. https://doi.org/10.1214/19-AOP1383

Information

Received: 1 December 2018; Revised: 1 May 2019; Published: May 2020
First available in Project Euclid: 17 June 2020

zbMATH: 07226355
MathSciNet: MR4112709
Digital Object Identifier: 10.1214/19-AOP1383

Subjects:
Primary: 60H15
Secondary: 35R60, 82B44, 82D60

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 3 • May 2020
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