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The two-dimensional KPZ equation in the entire subcritical regime

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Caravenna, Francesco, Sun, Rongfeng and Zygouras, Nikos (2020) The two-dimensional KPZ equation in the entire subcritical regime. Annals of Probability, 48 (3). pp. 1086-1127. doi:10.1214/19-AOP1383

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Official URL: http://dx.doi.org/10.1214/19-AOP1383

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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 and its strength is scaled as , then a transition occurs with explicit critical point . Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as , for sufficiently small . We prove here that the limit exists in the entire subcritical regime 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.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Statistics
Library of Congress Subject Headings (LCSH): Differential equations, Parabolic, Stochastic inequalities, Heat equation, White noise theory
Journal or Publication Title: Annals of Probability
Publisher: Institute of Mathematical Statistics
ISSN: 0091-1798
Official Date: May 2020
Dates:
DateEvent
May 2020Published
17 June 2020Available
25 June 2019Accepted
Date of first compliant deposit: 9 September 2019
Volume: 48
Number: 3
Page Range: pp. 1086-1127
DOI: 10.1214/19-AOP1383
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/R024456/1Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
20155PAWZBFundación Princesa de Asturiashttp://dx.doi.org/10.13039/501100006336
R-146-000-253-114National University of Singaporehttp://dx.doi.org/10.13039/501100001352
EP/R024456/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
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