Lipschitz-Killing Curvatures for Arithmetic Random Waves
Probability
2020-10-28 v1
Abstract
In this paper, we show that the Lipschitz-Killing Curvatures for the excursion sets of Arithmetic Random Waves (toral Gaussian eigenfunctions) are 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 centered 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.
Cite
@article{arxiv.2010.14165,
title = {Lipschitz-Killing Curvatures for Arithmetic Random Waves},
author = {Valentina Cammarota and Domenico Marinucci and Maurizia Rossi},
journal= {arXiv preprint arXiv:2010.14165},
year = {2020}
}