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Publication 18-CNA-031

Fluctuations of the solutions to the KPZ equation in dimensions three and higher

Alexander Dunlap
Department of Mathematics
Stanford University
Stanford, CA 94305, USA

Yu Gu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA

Lenya Ryzhik
Department of Mathematics
Stanford University
Stanford, CA 94305

Ofer Zeitouni
Department of Mathematics
Weizmann Institute of Science
POB 26, Rehovot 76100, Israel

Abstract: We prove, using probabilistic techniques and analysis on the Wiener space, that the large scale fluctuations of the KPZ equation in $d\geq 3$ with a small coupling constant, driven by a white in time and colored in space noise, are given by the Edwards-Wilkinson model. This gives an alternative proof, that avoids perturbation expansions, to the results of [Magnen-Unterberger 17].

Get the paper in its entirety as  18-CNA-031.pdf

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