Fluctuation in the spectrum of non-Hermitian i.i.d. random matrices

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Fluctuation in the spectrum of non-Hermitian i.i.d. random matrices
Giovedì 24 giugno 2021, ore 14:30, Giorgio Cipolloni (IST Austria)  terrà il seminario di Probabilità dal titolo "Fluctuation in the spectrum of non-Hermitian i.i.d. random matrices".

Abstract:
We consider a large non-Hermitian i.i.d. matrix X with real or complex entries, and we analyse its spectrum using Girko's formula. We will then show some applications of this approach proving: (i) edge universality (the non-Hermitian analogue of Tracy-Widom universality); (ii) Gaussian fluctuation of linear statistics of the eigenvalues for general test functions.
The proof relies on three main ingredients: (i) local law for product of resolvents of the Hermitisation of X, (ii) coupling of several weakly dependent Dyson Brownian motion, (iii) rigorous supersymmetric analysis.

Il seminario avrà luogo presso il Dipartimento di Matematica e Fisica
Largo San Leonardo Murialdo,1 - Pal.C - Stanza 211
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