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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Direction distribution for nodal components of random band-limited functions on surfaces
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by Suresh Eswarathasan and Igor Wigman PDF
Trans. Amer. Math. Soc. 373 (2020), 7383-7428 Request permission

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.).
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 7383-7428
  • MSC (2010): Primary 60G60; Secondary 53B20
  • DOI: https://doi.org/10.1090/tran/8153
  • MathSciNet review: 4155211