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math.PR2026
Phase Transitions in the Fluctuations of Functionals of Random Neural Networks
Simmaco Di Lillo, Leonardo Maini, Domenico Marinucci
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We…
math.PR2026
Limit theorems for anisotropic functionals of stationary Gaussian fields with Gneiting covariance function
Nikolai Leonenko, Leonardo Maini, Ivan Nourdin +1
We study non-linear additive functionals of stationary Gaussian fields over anisotropically growing domains in , including spatiotemporal settings, and establish Gaus…
math.PR2025
Malliavin differentiability for the excursion measure of a Gaussian field
Leonardo Maini
In this work, we investigate the Malliavin differentiability of the excursion volume of a Gaussian field. In particular, we prove that if the moments of the covariance kernel go to…