# Probability and Mathematical Physics Seminar

#### Free probability for random band matrices

Speaker: Benson Au, UC San Diego

Location: Warren Weaver Hall 512

Date: Friday, March 29, 2019, 11 a.m.

Synopsis:

Free probability provides a unifying framework for studying random multi-matrix models in the large $$N$$ limit. Typically, the purview of these techniques is limited to invariant or mean-field ensembles. Nevertheless, we show that random band matrices fit quite naturally in this framework. Our considerations extend to the infinitesimal level, where finer results can be stated for the $$\frac{1}{N}$$ correction. As an application, we consider the question of outliers for localized perturbations of our model.