Seminari del Dipartimento

 

Probabilita'

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

Giorgio Cipolloni


24-06-2021 - 14:30
Largo San Leonardo Murialdo,1 - Pal.C - Aula 211

 

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.


org: CAPUTO Pietro

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