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math.PR2009★ 3 cited
Universal Gaussian fluctuations of non-Hermitian matrix ensembles
Ivan Nourdin, Giovanni Peccati
We 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 a…
math.PR2009
Stein's method meets Malliavin calculus: a short survey with new estimates
Ivan Nourdin, Giovanni Peccati
We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability…
math.PR2009★ 2 cited
A multiple stochastic integral criterion for almost sure limit theorems
Bernard Bercu, Ivan Nourdin, Murad S. Taqqu
In this paper, we study almost sure central limit theorems for multiple stochastic integrals and provide a criterion based on the kernel of these multiple integrals. We apply our r…