“Gaussian Kinematic Formulas for Random Spherical Harmonics”
Venerdì 25 Novembre 2022, ore 15:30 - Aula 2AB40 e Zoom - Maurizia Rossi (Università Milano Bicocca)
In this talk we investigate the geometry of random spherical harmonics (Gaussian Laplace eigenfunctions on the round sphere). In particular we study the distribution, for large eigenvalues, of Lipschitz-Killing Curvatures (LKCs) of their excursion sets at any threshold. The main result we discuss is an asymptotic equivalence, in mean-square, between these functionals and the L2-norm of the random eigenfunction times a suitable map of the threshold (that vanishes at zero). This formula allows one to determine limiting distribution, correlation phenomena and moderate deviations for these LKCs, and generalizes – in the case of random spherical harmonics – those obtained by Adler and Taylor for their expected value. If time permits, we digress slightly to investigate the local geometry of spin spherical random fields, that is, random sections of the spin line bundles of the sphere.
This talk is mainly based on a number of joint works on random spherical harmonics with V. Cammarota, D. Marinucci and I. Wigman + a recent work on spin random fields written jointly with A. Lerario, D. Marinucci and M. Stecconi.