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

Speaker: 
Giorgio Cipolloni
Institution: 
Princeton Center for Theoretical Science, USA
Schedule: 
Wednesday, May 31, 2023 - 16:00
Location: 
A-132
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. 

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