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arXiv · 2302.06689

Mesoscopic averaging of the two-dimensional KPZ equation

Ran Tao
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Abstract

We study the limit of a local average of the KPZ equation in dimension $d=2$ with general initial data in the subcritical regime. Our result shows that a proper spatial averaging of the KPZ equation converges in distribution to the sum of the solution to a deterministic KPZ equation and a Gaussian random variable that depends solely on the scale of averaging. This shows a unique mesoscopic averaging phenomenon that is only present in dimension two. Our work is inspired by the recent findings by Chatterjee \cite{chatterjee2021weak}.

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Ran Tao. 2023-02-13. Mesoscopic averaging of the two-dimensional KPZ equation. https://doi.org/10.1007/s10955-023-03222-3

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