Wednesday, September 30, 2009
11:30 AM in LWSN 1142
Ivan Nourdin
Laboratoire de Probabilités, Université Paris 6, France

Universal Gaussian fluctuations of non-Hermitian matrix ensembles

Abstract

I will explain how to prove multi-dimensional central limit theorems for the spectral moments (of arbitrary degrees) associated with random matrices with real-valued i.i.d. entries, satisfying some appropriate moment conditions. The used techniques rely on a universality principle for the Gaussian Wiener chaos as well as some combinatorial estimates. Unlike other related results in the probabilistic literature, the fact that the law of the entries has a density with respect to the Lebesgue measure is not required. This talk is based on a joint work with Giovanni Peccati (Paris Ouest), and use an invariance principle obtained in a joint work with G. P. and Gesine Reinert (Oxford).