Ricevo ed inoltro
ricercaMatFis(a)mat.uniroma3.it
> gio 10/06/2021 15:38
> A:
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> - ricercaMatFis(a)mat.uniroma3.it
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> 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.
>