Student Probability/PDE Seminar: The Structure of Gibbs Measure with Low Complexity

Seminar | February 22 | 2:10-3:30 p.m. | 891 Evans Hall

 Kyeongsik Nam, UC Berkeley

 Department of Mathematics

I will talk about several different perspectives to analyze the structure of Gibbs measures with low complexity. The first perspective is a mean-field approximation to the free energy that appears in the variational formula, studied by Chatterjee and Dembo. As an application, one can compute the probability of large deviation events given by nonlinear functions with low complexity, for instance counting the number of subgraphs of the Erdos-Renyi random graphs in the sparse regime. Another direction is studied by Eldan, which says that Gibbs measure is approximately close to the mixture of product measures with an error term expressed in terms of the 'Gaussian-width gradient complexity'. The another possible method is recently introduced by Austin, which is based on purely information theoretical techniques. I will briefly mention these methods and discuss the strength of each perspective and relations between them.