Gaussian random interface models and discrete Green’s functions

Random interface models describe microscopic fluctuations of the boundary layer between two different substances. Mathematically, they are given by a probability measure on a suitable space of height functions. In several important cases, this measure is Gaussian, and its covariance can be understood as the Green’s function of some elliptic differential operator (or of its discretization).

In the talk, I will explain this connection and discuss a few examples. I will then describe how one can obtain estimates for these Green’s functions using tools from PDE theory and numerical analysis, and how these estimates can be used to establish some properties of the corresponding interface model.