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Scaling limit and convergence of smoothed covariance for gradient models with non-convex potential (1603.04703v1)
Published 15 Mar 2016 in math-ph, math.MP, and math.PR
Abstract: A discrete gradient model for interfaces is studied. The interaction potential is a non-convex perturbation of the quadratic gradient potential. Based on a representation for the finite volume Gibbs measure obtained via a renormalization group analysis by Adams, Koteck\'{y} and M\"uller in [AKM] it is proven that the scaling limit is a continuum massless Gaussian free field. From probabilistic point of view, this is a Central Limit Theorem for strongly dependent random fields. Additionally, the convergence of covariances, smoothed on a scale smaller than the system size, is proven.