Dipartimento di Scienze Statistiche

      il giorno lunedì 7 NOVEMBRE p.v. con inizio alle ore 9.00  - in presenza Sala 34 - IV piano del dipartimento e in modalità telematica  mediante accesso al seguente link:    https://uniroma1.zoom.us/j/86128803817?pwd=QStzMzB0ZGJLWFc5Z3FWaUJ0L1Q1QT09   PASSCODE: 395069     Abstract: In the last decade, lot of efforts have been devoted to the analysis of the high-frequency behaviour of geometric functionals (Lipschitz-Killing Curvatures, hereafter LKCs) for the excursion sets of Gaussian random fields. In particular we focus on random eigenfunctions on the unit sphere (spherical harmonics) and on the so-called needlets. The asymptotic behaviour of the expected values and variances of their LKCs are investigated and quantitative central limit theorems are established in the high energy limit.  In order to generalize these results to other manifolds, we also introduce a local study by considering subdomains of the sphere. Another interesting issue concerns the Gaussianity hypothesis of the random field. In this direction we introduce the Poisson random waves and we study Quantitative Central Limit Theorems when both the rate of the Poisson process and the energy (i.e., frequency) of the waves (eigenfunctions) diverge to infinity.