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
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Maurizia Rossi
Dipartimento di Matematica e Applicazioni
Università degli Studi di Milano-Bicocca