Ricevo ed inoltro
ricercaMatFis@mat.uniroma3.it
gio 10/06/2021 15:38
A:
- ricercaMatFis@mat.uniroma3.it
SEMINARIO Probabilita' Giorgio Cipolloni (IST Austria) Titolo: Fluctuation in the spectrum of non-Hermitian i.i.d. random matrices. Giovedi' 24 Giugno 2021 ORE 14:30 Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre Largo San Leonardo Murialdo,1 - Pal.C - Aula 211 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.