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

05/11/2023 1:30 pm - 2:30 pm
Benjamin McKenna Changji Xu
Harvard Science Center
Address: 1 Oxford Street, Cambridge MA 02138

Probability Seminar

Speaker: Giorgio Cipolloni (Princeton)

Title: How do the eigenvalues of a large non-Hermitian 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. 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.

Location: Science Center Room 232