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.