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The geometry of random eigenfunctions

20 ottobre 2016 ore 12:01 - 13:00

Aula 207, Sede di Viale Romania, 32

Speaker: Domenico Marinucci, Università degli Studi di Roma Tor Vergata

The geometry of random eigenfunctions

Abstract:

The characterization of the geometric properties for the excursion
sets of random fields on generic manifolds is a classical topic of
probability theory; it has been very much revived recently by the
discovery of the Gaussian Kinematic Formula by Adler and Taylor
(2007). This formula provides a fully explicit characterization of the
expected value for so-called Minkowski functionals of excursion sets
under very broad circumstances. In this talk, we review some very
recent results pointing at a generalization of this formula to the
variance of Minkowski functionals and to a corresponding Central Limit
Theorem, in the case of random eigenfunctions.


The talk is based on a recent paper with Valentina Cammarota;  if time
permits, we will also discuss some related results involving also
Giovanni Peccati, Maurizia Rossi and Igor Wigman.