*Lunedi 23 gennaio* *Ore 16:00, Aula di Consiglio* *Seminario di Probabilità e Statistica Matematica*

*Domenico Marinucci, Dipartimento di Matematica, Università di Roma Tor Vergata*

*Titolo: A Quantitative Central Limit Theorem for the Euler-Poincaré Characteristic of Random Spherical EigenfunctionsWe establish here a Quantitative Central Limit Theorem (in Wassersteindistance) for the Euler-Poincaré Characteristic of excursion sets ofrandom spherical eigenfunctions in dimension 2. Our proof is based upon adecomposition of the Euler-Poincaré Characteristic into differentWiener-chaos components: we prove that its asymptotic behaviour isdominated by a single term, corresponding to the chaotic component oforder two. As a consequence, we show how the asymptotic dependence on the threshold level u is fully degenerate, i.e. the Euler-PoincaréCharacteristic converges to a single random variable times a deterministicfunction of the threshold. This deterministic function has a zero at theorigin, where the variance is thus asymptotically of smaller order. Ourresults can be written as an asymptotic second-order Gaussian KinematicFormula for the excursion sets of Gaussian spherical harmonics.Based on a joint work with Valentina Cammarota.*

*Prossimo seminario: Valentina Cammarota, 31/1*

*Tutti gli interessati sono invitati ad intervenire.*

*Per richieste di informazioni scrivere a piccioni@mat.uniroma1.it.*