University of Connecticut

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Math Physics Learning Seminar
Giorgio Cipolloni, Institute Of Science And Technology, Austria
Fluctuation In The Spectrum Of Non-Hermitian I.I.D. Random Matrices

Friday, December 11, 2020
10:00am – 11:00am

Storrs Campus
online (please contact Masha)

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); (ii) Gaussian fluctuation of linear statistics of the eigenvalues for test function having 2+\epsilon derivatives. The proof relies on three main ingredients: (i) Rigorous SUSY; (ii) local law for product of resolvents of the Hermitisation of X at two different spectral parameters, (iii) coupling of several dependent Dyson Brownian motions.


Analysis Learning Seminar (primary), Math Physics Learning Seminar, UConn Master Calendar

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