ricercaMatFis@mat.uniroma3.it
gio 10/06/2021 15:38

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•  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.