Tangent nodal sets for random spherical harmonics

Eswarathasan, Suresh 2019. Tangent nodal sets for random spherical harmonics. Presented at: CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, Montreal, Canada, 2016. Published in: Yaiza, Canzani, Linan, Chen and Dmitry, Jakobson eds. Probabilistic Methods in Geometry, Topology and Spectral Theory (Contemporary Mathematics). Centre de Recherches Mathématiques Lecture Notes and Proceedings Series. , vol.739 American Mathematical Society, pp. 17-43. 10.1090/conm/739/14892 Item availability restricted.

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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:	Conference or Workshop Item (Paper)
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	American Mathematical Society
ISBN:	9781470441456
Date of First Compliant Deposit:	31 December 2018
Date of Acceptance:	11 December 2018
Last Modified:	13 Nov 2024 19:45
URI:	https://orca.cardiff.ac.uk/id/eprint/117912

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

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