On the correlation between nodal and boundary lengths for random spherical harmonics
Mathematical Physics
2019-02-18 v1 math.MP
Probability
Abstract
We study the correlation between the nodal length of random spherical harmonics and the measure of the boundary for excursion sets at any non-zero level. We show that the correlation is asymptotically zero, while the partial correlation after controlling for the random -norm on the sphere of the eigenfunctions is asymptotically one.
Cite
@article{arxiv.1902.05750,
title = {On the correlation between nodal and boundary lengths for random spherical harmonics},
author = {Domenico Marinucci and Maurizia Rossi},
journal= {arXiv preprint arXiv:1902.05750},
year = {2019}
}