KPZ equation from a class of nonlinear SPDEs in infinite volume
Probability
2025-12-30 v3 Mathematical Physics
Analysis of PDEs
math.MP
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.
Keywords
Cite
@article{arxiv.2507.10545,
title = {KPZ equation from a class of nonlinear SPDEs in infinite volume},
author = {Kevin Yang},
journal= {arXiv preprint arXiv:2507.10545},
year = {2025}
}
Comments
minor revisions, comments welcome!