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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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).