Tangent nodal sets for random spherical harmonics

Eswarathasan, Suresh 2018. Tangent nodal sets for random spherical harmonics. [Online]. arXiv. Available at: https://arxiv.org/abs/1809.01595

Preview

PDF - Submitted Pre-Print Version Download (368kB) | Preview

Abstract

In this note, we consider a fixed vector field $V$ on $S^2$ and study the distribution of points which lie on the nodal set (of a random spherical harmonic) where $V$ 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 $V$. This demonstrates, in some form, a universality for vector fields up to lower order terms.

Item Type:	Website Content
Date Type:	Submission
Status:	Unpublished
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	arXiv
Last Modified:	19 Nov 2024 07:30
URI:	https://orca.cardiff.ac.uk/id/eprint/114680

Available Versions of this Item

• Tangent nodal sets for random spherical harmonics. (deposited 09 Oct 2018 11:15) [Currently Displayed]
  • Tangent nodal sets for random spherical harmonics. (deposited 07 Jan 2019 14:15)

Actions (repository staff only)

Edit Item