Quantitative universality in random matrix theory

This project proposal studies the local eigenvalue behavior of several random matrix models.

We aim to strengthen the edge universality by establishing a broad framework to derive quantitative convergence rate estimates for the fluctuations of the extremal eigenvalues of Wigner random matrices and other models motivated from mathematical statistics and random graph theory.

In analogy with the standard central limit theorem, these results can be viewed as Berry-Esseen theorems for the convergence in distribution to the universal laws given by the Tracy-Widom distributions.

Such quantitative estimates are not only of interest from a theoretical perspective, but also justify the accuracy of many hypothesis tests based on extremal eigenvalues.With the project grant, the project leader intends to hire a PhD student for a duration of five years, who will work together with the PI on several projects outlined in the research plan.

The fifth year will be supported by the department of mathematics at KTH. The funding will also be used to pay parts of the project leader´s salary. The budget further includes costs for office space, travel expenses and overhead costs.