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KPZ equation from a class of nonlinear SPDEs in infinite volume

Published 14 Jul 2025 in math.PR, math-ph, math.AP, and math.MP | (2507.10545v1)

Abstract: We study a class of nonlinear Ginzburg-Landau SPDEs in infinite-volume. We show that under a weakly asymmetric scaling, their solutions converge to that of the KPZ equation. The key technical innovation is the analysis of a stochastic heat kernel for the SPDE of interest, which allows for a multi-scale "localization" to the compact setting.

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