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Tangent nodal sets for random spherical harmonics

Eswarathasan, Suresh 2018. Tangent nodal sets for random spherical harmonics. arXiv , arXiv:1809.01595.

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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: Article
Date Type: Submission
Status: Unpublished
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Publisher: Cornell University
Last Modified: 10 Mar 2020 19:24
URI: http://orca.cf.ac.uk/id/eprint/114680

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