CMSA Probability Seminar: How do the eigenvalues of a large non-Hermitian random matrix behave?


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May 11, 2023 1:30 pm - 2:30 pm
Science Center 232

Giorgio Cipolloni - Princeton University

**note unusual day, time and location**

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.