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The geometry of random eigenfunctions

  • Date December 1, 2016
  • Hour 3 pm
  • Room GSSI Main Lecture Hall
  • Speaker Domenico Marinucci (University of Roma Tor Vergata)

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.