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
ajdunl2@stanford.edu

Yu Gu
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213, USA
yug2@andrew.cmu.edu

Lenya Ryzhik
Department of Mathematics
Stanford University
Stanford, CA 94305
ryzhik@math.stanford.edu

Ofer Zeitouni
Department of Mathematics
Weizmann Institute of Science
POB 26, Rehovot 76100, Israel
ofer.zeitouni@weizmann.ac.il

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].

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