Special Oliver Club
Giorgio CipolloniPrinceton University
How do the eigenvalues of a large non-Hermitian random matrix behave?
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 ˙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.