AVVISO di SEMINARIO

Title: The Geometry of Time-Dependent Spherical Random Fields

Prof. Domenico Marinucci

Università di Roma Tor Vergata

Abstract: The investigation of the behaviour for geometric functionals of random fields on manifolds has drawn recently considerable attention. In this talk, we consider fluctuations over time for the excursion area and the length of level curves of time-dependent Gaussian spherical random fields. We focus on both long and short memory assumptions; in the former case, we show that the fluctuations are dominated by a single component, corresponding to a second-order chaos evaluated on a subset of the multipole components for the random field. We prove the existence of cancellation points where the variance is asymptotically of smaller order; these points may not include the nodal case u=0, in marked contrast with recent results on the high-frequency behaviour of nodal lines for random eigenfunctions with no temporal dependence. In the short memory case, we show that all chaoses contribute in the limit, no cancellation occurs and a Central Limit Theorem can be established by Fourth-Moment Theorems and a Breuer-Major argument.

The talk is based on joint works with Maurizia Rossi and Anna Vidotto.

Il seminario si terrà il giorno 13 Settembre 2022 ore 12:00 nella Aula E terzo livello del Dipartimento Matematica e Applicazioni, Università di Napoli FEDERICO II, Complesso di Monte Sant'Angelo, Via Cintia, Napoli.

Link al seminario su Teams:

https://teams.microsoft.com/l/meetup-join/19%3aMQ4RZDBo_0G-K_PHxKtktVYAczOGb...

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