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arXiv · 2507.10545

KPZ equation from a class of nonlinear SPDEs in infinite volume

Kevin Yang
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Abstract

We study a general class of nonlinear Ginzburg-Landau SPDEs in infinite volume under weak nonlinearity scaling and with non-equilibrium initial data. We derive the KPZ equation as a continuum limit of these equations. This makes rigorous the original derivation of the KPZ equation from physics in the full-space setting, which was a problem posed by Hairer-Quastel '18. Our analysis is based on a stochastic heat kernel for a linearization of said SPDEs.

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Kevin Yang. 2025-07-14. KPZ equation from a class of nonlinear SPDEs in infinite volume. https://arxiv.org/abs/2507.10545

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