Tuesday, February 4, 2020 | 2:30PM | Yost 306

Title: Convergence Rates for Determinantal Point Process induced Random Variables

Abstract

A central theme in probability is studying the convergence of collections of random variables to limits. Asymptotic statements such as the central limit theorem and the law of large numbers are foundational results. Often it is interesting to go further and obtain more refined information in the form of a rate of convergence. Classical models from random matrix theory have famous limiting distributions, usually focused on the distributions of eigenvalues of a certain random matrix model. Meckes and Meckes have shown how to obtain a rate of convergence for one such family of eigenvalue random variables arising from the Circular Unitary Ensemble (CUE). I will show some provisional results of a similar nature for a different random matrix ensemble, the Gaussian Unitary Ensemble (GUE). I will talk about some of the necessary background, describe the differences between the proofs for the GUE and CUE, give one result for the GUE, and (hopefully) a second result for the GUE (assuming it is finished in the next couple days).