Dear all, It is a pleasure to announce the following probability seminar Speaker:* Leonardo Maini* *(Univ. Roma Tor Vergata)* Date and place: *Monday** 23 February 2.30pm-3:30 pm -- **ATLAS building, room* *U1-04*, *Univ. Milano-Bicocca* (Piazza della Scienza 1, Milano) . Title: *Non-universal fluctuations for functionals of random neural networks* Abstract: We establish central and non-central limit theorems for sequences of functionals of the limiting Gaussian output of random neural networks on the sphere. We show that the asymptotic behaviour is determined by the fixed points of the covariance kernel and leads to three possible regimes: convergence to the same functional evaluated at a limiting Gaussian field, convergence to a Gaussian distribution, or convergence to a spherical Rosenblatt/Hermite-type distribution. More generally, we show that the transition between these behaviours is governed by the uniforme order of integrability (up to controlled errors) of the renormalized covariance function. This mechanism is closely related to what happens for Gaussian fields with regularly varying covariances at infinity in the Euclidean setting, and reveals an analogous structure on the sphere. Based on a joint work with S. Di Lillo and D. Marinucci. Best wishes, Maurizia Rossi -- Maurizia Rossi Dipartimento di Matematica e Applicazioni Università degli Studi di Milano-Bicocca https://mauriziarossi.wordpress.com