Dear Colleagues, we would like to invite you to the following seminar by Leonardo Maini (Université du Luxembourg) to be held Wednesday, June 22nd, in Aula Contini, at Scuola Normale Superiore in Pisa.
The seminar will take place in full presence (speaker included), but it will be streamed via Google Meets, link below.
The organizers, A. Agazzi and F. Grotto
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Location: *Aula Contini*, Scuola Normale Superiore, Pisa Google Meet Link: https://meet.google.com/gji-phwo-vbg
Time: June 22nd 2022, 14:00-15:00 CET Speaker: Leonardo Maini (Université du Luxembourg) 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 is to show that this can be a misleading intuition. To do 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 Ivan Nourdin (University of Luxembourg).