Mihai Nica (Guelph)

Title: A Gaussian integral formula for the Hermite polynomials: Theory and Applications.

Abstract: The Hermite polynomials arise throughout probability theory, from Dyson’s Brownian motion to classical asymptotic expansions, and they have long been a key tool in applied analysis. In this talk, I will showcase a Gaussian expectation formula that demystifies some of the theory and applications of the Hermite polynomials. Of particular interest will be using the Hermite polynomials to obtain higher order approximations to large neural networks, in the limit that the number of neurons goes to infinity. This talk is based on this joint work with Janosch Ortmann (UQAM) available at https://arxiv.org/abs/2508.13910