Special Oliver Club

Giorgio CipolloniPrinceton University
How do the eigenvalues of a large non-Hermitian random matrix behave?

Tuesday, March 28, 2023 - 4:00pm
Malott 532 (Lounge)

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 $X$.

Refreshments will be served at 3:30 PM.