Cari colleghi,
vi annuncio che giovedì 27 novembre, alle ore 14:30 precise, nell'aula
Beltrami del Dipartimento di Matematica dell'Universita' di Pavia,
la Dott. Maurizia ROSSI
(Università di Roma Tor Vergata) terra' un seminario dal titolo
*"Quantitative Central Limit Theorems for Nonlinear Functionals of
RandomEigenfunctions on $\mathbb S^d$, $d\ge 2$".*
Distinti saluti,
Raffaella Carbone
-----------------
*ABSTRACT*
*We investigate Stein-Malliavin approximations for nonlinear functionals of
geometric interest for random eigenfunctions on the unit d-dimensional
sphere Sd, d ≥ 2. All our results are established in the high energy limit,
i.e. as the corresponding eigenvalues diverge. In particular, we prove a
quantitative Central Limit Theorem for the ex- cursion volume of Gaussian
eigenfunctions; this goal is achieved by means of several results of
independent interest, concerning the asymptotic analysis for the variance
of moments of Gaussian eigenfunctions, the rates of convergence in various
probability metrics for Hermite subordinated processes, and quantitative
Central Limit Theo- rems for arbitrary polynomials of finite order or
general, square-integrable, nonlinear transforms. Some related issues were
already considered in the literature for the 2- dimensional case S2; our
results are new or improve the existing bounds even in this special
circumstances. Proofs are based on the asymptotic analysis of moments of
all order for Gegenbauer polynomials, and make extensive use of the recent
literature on so-called fourth-moment theorems by Nourdin and Peccati. This
talk is based on the paper Stein-Malliavin Approximations for Nonlinear
Func- tionals of Random Eigenfunctions on Sd, joint work with Domenico
Marinucci.----------------*
Raffaella Carbone, PhD
Ricercatore di Probabilità e Statistica Matematica
Dipartimento di Matematica dell'Università degli Studi di Pavia