HET Seminar |Giorgio Cipolloni , Princeton| “ How do the eigenvalues of a large non-Hermitian random matrix behave? ” | PCTS & Zoom

Feb 20, 2023, 2:30 pm2:30 pm
PCTS & Zoom



Event Description

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.