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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
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 | |||||||||||||||
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| 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: |
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| 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: |
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