In this talk, we will consider a classical model of random interfaces known as the grad phi (or Ginzburg-Landau) model. The model first received rigorous consideration in the work of Brascamp-Lieb-Lebowitz in 1975. Since then, it has been extensively studied by the mathematical community and various aspects of the model have been investigated regarding for instance the localization and delocalization of the interface, the hydrodynamical limit, the scaling limit, large deviations etc. Most of these results were originally established under the assumption that the potential encoding the definition of the model is uniformly convex, and it has been an active line of research to extend these results beyond the assumption of uniform convexity. In this talk, we will introduce the model, some of its main properties, and discuss a result of localization and delocalization for a class of convex (but not uniformly convex) potentials.
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Thierry Bodineau, Pieter Lammers, Yilin Wang