Speaker: Domenico Marinucci, Università degli Studi di Roma Tor Vergata
The geometry of random eigenfunctions
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.