Large-scale limit of interface fluctuation models

Abstract

We extend the weak universality of KPZ in [Hairer-Quastel] 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.

arXiv comment64 page; some typos fixed

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Cited by in corpus (4)

• A variational method for ${\Phi }_3^4$
• The dynamical sine-Gordon model in the full subcritical regime
• Some recent progress in singular stochastic PDEs
• Sharp convergence of nonlinear functionals of a class of Gaussian random fields