# Probability and Mathematical Physics Seminar

#### How do the eigenvalues of a large random matrix behave?

Speaker: Giorgio Cipolloni, Princeton

Location: Warren Weaver Hall 1302

Date: Friday, September 23, 2022, 11:10 a.m.

Synopsis:

We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a non-natural scale, due to strong correlations between the eigenvalues.
Then, motivated by the long time behaviour of the ODE \dot{u}=Xu, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X.