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Gaussian fluctuations from the 2D KPZ equation

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Abstract

We prove the two dimensional KPZ equation with a logarithmically tuned nonlinearity and a small coupling constant, scales to the Edwards–Wilkinson equation with an effective variance.

Keywords

KPZ equation Edwards–Wilkinson equation Feynman–Kac formula 

Mathematics Subject Classification

35R60 60H07 60H15 

Notes

Acknowledgements

We would like to thank Li-Cheng Tsai for his initial involvement in this project and multiple inspiring discussions. We thank Nikolaos Zygouras for some helpful discussions, and two anonymous referees for a very careful reading of the manuscript and many helpful suggestions to improve the presentation. The research is supported by NSF Grant DMS-1613301/1807748/1907928 and the Center for Nonlinear Analysis of CMU.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsCarnegie Mellon UniversityPittsburghUSA

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