Monday 23 February 2026, at 2:30 pm in Room U1-04 (U1 Building | Piazza della Scienza 1, Milano), Leonardo Maini (University of Rome "Tor Vergata") will hold the following talk
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.
All interested are invited to participate