*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(a)mat.uniroma1.it.*