Disordered systems are mathematical models (typically of the physical world) that are governed by random variables.  These models have offered insights into a diverse array of research problems, and have also brought about a great number of powerful mathematical tools.  The through line to the subject is the essential role played by probability theory, a…

Gibbs measures are ubiquitous in statistical mechanics and probability theory. In this talk I will discuss two types of classes of Gibbs measures – random line ensembles and triangular particle arrays, which have received considerable attention due, in part, to their occurrence in integrable probability. Gibbsian line ensembles can be thought of as collections of…

In the study of disordered quantum systems, it is believed that a strong dichotomy should occur between two phases: a delocalized (or conducting) phase and a localized (or insulating) phase. While this is far from being proved in all generality, the study of large symmetric random matrices, which model simple systems, allows us to describe…

A classical result due to Dobrushin (1956) yields the central limit theorem for partial sums of functionals of inhomogeneous ("sufficiently contracting'') Markov chains. In the talk we will restrict to bounded functionals of uniformly elliptic inhomogeneous Markov chains, for which we can obtain: A Berry-Esseen theorem (optimal rates in the Central limit theorem); Correction terms of…