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arXiv · 1812.05768

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

Alexander Dunlap·Yu Gu·Lenya Ryzhik·Ofer Zeitouni
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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 and Unterberger \cite{magnen2017diffusive}.

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Alexander Dunlap, Yu Gu, Lenya Ryzhik, Ofer Zeitouni. 2018-12-14. Fluctuations of the solutions to the KPZ equation in dimensions three and higher. https://arxiv.org/abs/1812.05768

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