Large scale limit of interface fluctuation models

We extend the weak universality of KPZ in Hairer and Quastel [Forum Math. Pi 6 (2018) e3] to weakly asymmetric interface models with general growth mechanisms beyond polynomials. A key new ingredient is a pointwise bound on correlations of trigonometric functions of Gaussians in terms of their polynomial counterparts. This enables us to reduce the problem of a general nonlinearity with sufficient regularity to that of a polynomial.