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Non-Gaussian Surface Pinned by a Weak Potential J.-D. Deuschel and Y. Velenik Probab. Theory Relat. Fields 116, 359-377 (2000). We consider a model of a two-dimensional interface of the (continuous) SOS type, with finite-range, strictly convex interactions. We prove that, under an arbitrarily weak pinning potential, the interface is localized. We consider the cases of both square well and $\delta potentials. Our results extend and generalize previous results for the case of nearest-neighbours Gaussian interactions by Dunlop et al and Bolthausen and Brydges. We also obtain the tail behaviour of the height distribution, which is not Gaussian. Key words: Non-Gaussian gradient model, SOS model, pinning, decay of correlations, Brascamp-Lieb inequality. Files: PDF, Published version, bibtex