****************************************************** SEMINARI DI PROBABILITA' E STATISTICA DIPARTIMENTO DI MATEMATICA G. PEANO UNIVERSITA' DEGLI STUDI DI TORINO ******************************************************

Lunedì 15 Dicembre 2014 alle ore 11:00 in Aula S, presso il Dipartimento di Matematica "G. Peano" dell'Università degli Studi di Torino, Via Carlo Alberto 10,

La Dott.ssa VALENTINA CAMMAROTA (Department of Mathematics, Università degli Studi di Roma "Tor Vergata")

terrà un seminario dal titolo

ON THE DISTRIBUTION OF THE CRITICAL VALUES OF RANDOM SPHERICAL HARMONICS

Abstract:

We study the limiting distribution of critical points and extrema of random spherical harmonics, in the high energy limit. In particular, we first derive the density functions of extrema and saddles; we then provide analytic expressions for the variances and we show that the empirical measures in the high-energy limits converge weakly to their expected values. Our arguments require a careful investigation of the validity of the Kac-Rice formula in nonstandard circumstances, entailing degeneracies of covariance matrices for first and second derivatives of the processes being analysed.

Joint paper with Domenico Marinucci (Università degli studi di Roma "Tor Vergata") and Igor Wigman (King's College, London)

Tutti gli interessati sono invitati a partecipare.

-- Federico Polito

Department of Mathematics University of Torino Via Carlo Alberto, 10 10123, Torino, Italy Email: federico.polito@unito.it Tel: +39 011 6702937 Web: www.federicopolito.it