Talk on Friday 2:10-3:00 pm in Fields 309

[Benjamin Landon]

Hi all,

We will have our first talk of the year on Friday Oct 6.  Our usual schedule will be Mondays 3-4 pm, this Friday is exceptional.

The talk on Friday will be in Fields 309 (the library upstairs).

Speaker: Giorgio Cipolloni (Princeton)

Date and time: Friday, Oct 6, 2:10-3:00pm, Fields 309

Title:  How do the eigenvalues of a large random matrix behave?

Abstract:

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. We also study the space--time correlations of those eigenvalues.

Then, motivated by the long-time behaviour of the ODE u˙=Xu, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X, and prove the universality of their Gumbel fluctuations.