KPZ equation from a class of nonlinear SPDEs in infinite volume

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 [31] in the full-space setting, which was a problem posed in [27]. Our analysis is based on a stochastic heat kernel for a linearization of said SPDEs.