Universal Gaussian fluctuations of non-Hermitian matrix ensembles

Stochastics Seminar
Tuesday, November 3, 2009 - 4:00pm for 1 hour (actually 50 minutes)
Skiles 255 (Note unusual time and location)
Ivan NOURDIN – Paris VI
Yuri Bakhtin
My aim is to 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 techniques I will use rely on a universality principle for the Gaussian Wiener chaos as well as some combinatorial estimates. Unlike other related results in the probabilistic literature, I will not require that the law of the entries has a density with respect to the Lebesgue measure. The talk is based on a joint work with Giovanni Peccati, and use an invariance principle obtained in a joint work with G. P. and Gesine Reinert