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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Variance of the number of zeros of dependent Gaussian trigonometric polynomials
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by Louis Gass
Proc. Amer. Math. Soc. 151 (2023), 2225-2239
DOI: https://doi.org/10.1090/proc/16303
Published electronically: February 28, 2023

Abstract:

We compute the variance asymptotics for the number of real zeros of trigonometric polynomials with random dependent Gaussian coefficients and show that under mild conditions, the asymptotic behavior is the same as in the independent framework. In fact our proof goes beyond this framework and makes explicit the variance asymptotics of various models of random Gaussian processes. Our proof relies on intrinsic properties of the Kac–Rice density in order to give a short and concise proof of variance asymptotics.
References
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Bibliographic Information
  • Louis Gass
  • Affiliation: Université de Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
  • Email: louis.gass@ens-rennes.fr
  • Received by editor(s): March 29, 2022
  • Received by editor(s) in revised form: September 7, 2022, and September 22, 2022
  • Published electronically: February 28, 2023
  • Additional Notes: This work was supported by the ANR grant UNIRANDOM, ANR-17-CE40-0008.
  • Communicated by: Zhen-Qing Chen
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 2225-2239
  • MSC (2020): Primary 60G15, 60G57
  • DOI: https://doi.org/10.1090/proc/16303
  • MathSciNet review: 4556213