Tangent nodal sets for random spherical harmonics
Spectral Theory
2018-09-12 v2 Analysis of PDEs
Differential Geometry
Abstract
In this note, we consider a fixed vector field on and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where is also tangent. We show that the expected value of the corresponding counting function is asymptotic to the eigenvalue with a leading coefficient that is independent of the vector field . This demonstrates, in some form, a universality for vector fields up to lower order terms.
Cite
@article{arxiv.1809.01595,
title = {Tangent nodal sets for random spherical harmonics},
author = {Suresh Eswarathasan},
journal= {arXiv preprint arXiv:1809.01595},
year = {2018}
}
Comments
26 pages. Minor changes with equation numbering. Updated introduction. All comments are welcome