Probability and Mathematical Physics Seminar

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Gradient interface models are lattice models from statistical mechanics that arise when describing the microscopic fluctuations of interfaces in nature. While many of their features are believed to be universal, rigorous results are often known only for specific classes of models. I will survey some of these results, and then describe two recent advances: The behavior of the maximum for two-dimensional fields with strictly convex interaction, and scaling limits of the fields for general monotone interactions with quadratic growth.