Dear Colleagues, We would like to invite you to the following seminar, by Claudio Macci on Friday 30 january 2026, starting at 11 am. Titles and abstract are below. With best regards, Enrico Priola ---- Friday 30 january 2026 at 11 am - Aula Beltrami, via Ferrata 5, Università di Pavia Link Zoom https://unipv-it.zoom.us/j/95012043373?pwd=VaSaGaIDZQnbVWixaqeDzI4uhY5H2I.1 ID riunione: 950 1204 3373 Codice d’accesso: 789010 Speaker: Claudio Macci (Università di Roma Tor Vergata) TITLE Some recent large deviation results on random neural networks ABSTRACT In this talk, I consider random neural networks with Gaussian weights and biases. A well-known result (proved under various assumptions in several references) concerns the convergence in distribution of the network output, in the infinite-width limit, to a centered Gaussian process with i.i.d. components (with the depth $L$ kept fixed). I will present some large deviation results describing a collapse of the network output (which, as expected, converges to the zero vector) when it is multiplied by a scaling factor tending to zero; see [1], where moderate deviations are also studied. In the final part, I will briefly outline some results in a very recent work (see [2]) concerning the deep limit (that is, as $L\to\infty$) for a generic component of the Gaussian process mentioned above. REFERENCES [1] C. Macci, B. Pacchiarotti, G.L. Torrisi. Journal of Applied Probability (2026), in press. [2] S. Di Lillo, C. Macci, B. Pacchiarotti. Submitted, and available on arxiv. -- Enrico Priola Dipartimento di Matematica, Università di Pavia Via Adolfo Ferrata 5, 27100 Pavia tel +39 0382 985639