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Transactions of the American Mathematical Society

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Direction distribution for nodal components of random band-limited functions on surfaces


Authors: Suresh Eswarathasan and Igor Wigman
Journal: Trans. Amer. Math. Soc. 373 (2020), 7383-7428
MSC (2010): Primary 60G60; Secondary 53B20
DOI: https://doi.org/10.1090/tran/8153
Published electronically: July 29, 2020
MathSciNet review: 4155211
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Abstract: Let $(\mathcal {M},g)$ be a smooth compact Riemannian surface with no boundary. Given a smooth vector field $V$ with finitely many zeros on $\mathcal {M}$, we study the distribution of the number of tangencies to $V$ of the nodal components of random band-limited functions. It is determined that in the high-energy limit, these obey a universal deterministic law, independent of the surface $\mathcal {M}$ and the vector field $V$, that is supported precisely on the even integers $2 \mathbb {Z}_{> 0}$.


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Additional Information

Suresh Eswarathasan
Affiliation: Department of Mathematics, Dalhousie University, Chase Building, Halifax, Nova Scotia, Canada
MR Author ID: 951602
Email: sr766936@dal.ca

Igor Wigman
Affiliation: Department of Mathematics, King’s College London, Strand Campus, London, United Kingdom
MR Author ID: 751303
ORCID: 0000-0002-6152-4743
Email: igor.wigman@kcl.ac.uk

Received by editor(s): October 29, 2019
Received by editor(s) in revised form: March 4, 2020, and March 15, 2020
Published electronically: July 29, 2020
Additional Notes: The research leading to these results received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC grant agreement n$^{\text {o}}$ 335141 (I.W.).
Article copyright: © Copyright 2020 American Mathematical Society