This seminar will be presented in hybrid mode.  The speaker will deliver his talk in person.

Title: Spectral central limit theorem for additive functionals of Gaussian fields

Abstract: We consider a centered, continuous, stationary, Gaussian field on the Euclidean space and a sequence of non-linear additive functionals of the field. Since the pioneering works from the 80s by Breuer, Dobrushin, Major, Rosenblatt, Taqqu and others, central and non-central limit theorems for this kind of functionals have never ceased to be refined. The common intuition is that the limit is Gaussian when we have short-memory and non-Gaussian when we have long-memory and the Hermite rank R is different from 1. Our goal in this talk is to explain why this intuition is not always true. For that, we introduce a spectral central limit theorem, which highlights a variety of situations where the limit is Gaussian in a long-memory context with R different from 1. Our main mathematical tools are the Malliavin-Stein method and Fourier analysis. The talk is based on a joint work with Leonardo Maini (University of Luxembourg).

The talk will be followed by refreshments in the Huxley Common Room at 4pm.