PC Seminar: Some new results on non-convex random gradient Gibbs measures

Abstract: In this talk we consider a class of gradient models with and without disorder. The simplest example of such models is the (lattice) Gaussian Free Field, which has quadratic potential V(s)=s^2/2. A well known result of Funaki and Spohn asserts that, for any uniformly-convex potential V, the possible infinite-volume measures of this type are uniquely characterized by the tilt, which is a vector in R^d. We show that this model is disorder relevant with respect to the question of uniqueness of gradient Gibbs measures when disorder is added to the system. We also discuss some functional inequalities connected to the model (such as Poincaré and log-Sobolev inequalities).

No previous knowledge of gradient models or statistical mechanics will be assumed in the talk.

This is based on joint works with Simon Buchholz and Florian Schweiger.

This is a seminar in our seminar series on Probability and Combinatorics (PC).