"Universality of the Gaussian Wiener chaos" Giovanni Peccati, Université Paris Ouest We will prove that the Gaussian Wiener chaos has a universal character with respect to (possibly multidimensional) Gaussian approximations. Our techniques are based on a combination of Stein's method and Malliavin calculus, as well as on Lindeberg-type invariance principles due to Rotar' (1979) and Mossel, O'Donnel and Oleszkiewicz (2008). Several applications (for example, to harmonic analysis of spherical fields and power variations of fractional processes) will be evoked. In particular, we will apply our main results in order to establish universal Gaussian fluctuations for general (possibly discrete) non-Hermitian random matrix ensembles.
This talk is based on joint works with I. Nourdin (Paris VI) and G. Reinert (Oxford).