KPZ equation from a class of nonlinear SPDEs in infinite volume
Kevin Yang
Published: 2025/7/14
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 result holds for a large class of potentials, nonlinearities, and essentially any (non-equilibrium) initial data for the limit KPZ equation. The main technical innovation is the analysis of a stochastic heat kernel for the SPDE of interest.