Title: Extremes of Gaussian random interfaces
Authors: Alessandra Cipriani - TU Delft (Netherlands) [presenting]
Abstract: Random interfaces arise naturally as separating surfaces between two different thermodynamic phases or states of matter, for example oil and water. When one views them as a field of random heights, it is natural to investigate the behavior of their rescaled maxima. We will review the current state of the art concerning the limiting behavior of extrema of Gaussian models that play a major role in statistical mechanics: the discrete Gaussian free field (DGFF), the membrane model (MM), and the $(\nabla+\Delta)$-model, which represents a mixture between DGFF and MM. We will present their similarities and differences, and show that the study of their extrema is connected with the theory of partial differential equations and numerical analysis.