UBC Probability Seminar: Andrea Montanari (Online)

Starting in the 70's, physicists have introduced a class of random energy functions and corresponding random probability distributions (Gibbs measures), the are known as mean-field spin glasses. Over the years, it has become increasingly clear that a broad array of canonical models in random combinatorics and (more recently) high-dimensional statistics are in fact examples of mean-field spin glasses, and can be studied using tools developed in that area.

Crucially, these new application domains have brought up a number of interesting new questions that were not central from the viewpoint of stat. physics. These lectures will focus on these new questions: (i) Statistical questions: what is the accuracy or uncertainty associated to a certain statistical method? (ii) Computational questions: can we efficiently compute marginals of a Gibbs measure? Can we generate low-energy configurations?

Lecture 1: High dimensional statistics. General setting and key questions. The role of sharp asymptotic. Examples and general phenomena.