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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). American Mathematical Society, pp. 17-43. 10.1090/conm/739/14892
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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: 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: 20 May 2020 12:09

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