A0628
Title: Lipschitz-Killing curvatures for arithmetic random waves
Authors: Valentina Cammarota - Sapienza University of Rome (Italy) [presenting]
Domenico Marinucci - University of Rome Tor Vergata (Italy)
Maurizia Rossi - Universite du Luxembourg (Luxembourg)
Abstract: The purpose is to show that the Lipschitz-Killing Curvatures for the excursion sets of Arithmetic Random Waves (toral Gaussian eigenfunctions) is dominated, in the high-frequency regime, by a single chaotic component. The latter can be written as a simple explicit function of the threshold parameter times the centred norm of these random fields; as a consequence, these geometric functionals are fully correlated in the high-energy limit. The derived formulae show a clear analogy with related results on the round unit sphere and suggest the existence of a general formula for geometric functionals of random eigenfunctions on Riemannian manifolds.
