Gaussian random interface models and discrete Green’s functions

Date: Wed. December 07, 2022:
Event: FAU DCN-AvH Seminar
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Title: FAU DCN-AvH Seminar “Gaussian random interface models and discrete Green’s functions”

Speaker: Dr. Florian Schweiger
Affiliation: Weizmann Institute of Science (Israel)

Abstract. 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 on a lattice. In several important cases, this measure is Gaussian, and its covariance can be understood as the Green’s function of the discretization of some elliptic differential operator.

In the talk, I will explain this connection and discuss various 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.


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