THERMODYNAMIC AND SCALING LIMITS OF THE NON-GAUSSIAN MEMBRANE MODEL

Abstract

We characterize the behavior of a random discrete interface φ on (Formula Presented)with energy(Formula Presented), where ∆ is the discrete Laplacian and V is a uniformly convex, symmetric, and smooth potential. The interface φ is called the non-Gaussian membrane model. By analyzing the Helffer–Sjöstrand representation, associated to ∆φ, we provide a unified approach to continuous scaling limits of the rescaled and interpolated interface in dimensions d = 2, 3, Gaussian approximation in negative regularity spaces for all d ≥ 2, and the infinite volume limit in d ≥ 5.