The Scaling Limit of the (∇ + Δ) -Model
Alessandra Cipriani (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Biltu Dan (Indian Statistical Institute)
Rajat Subhra Hazra (Indian Statistical Institute)
More Info
expand_more
Abstract
In this article we study the scaling limit of the interface model on Zd where the Hamiltonian is given by a mixed gradient and Laplacian interaction. We show that in any dimension the scaling limit is given by the Gaussian free field. We discuss the appropriate spaces in which the convergence takes place. While in infinite volume the proof is based on Fourier analytic methods, in finite volume we rely on some discrete PDE techniques involving finite-difference approximation of elliptic boundary value problems.