Abstract
We show that the number of real roots of random trigonometric polynomials with i.i.d. coefficients, which are either bounded or satisfy the logarithmic Sobolev inequality, satisfies an exponential concentration of measure.
Nous montrons que le nombre des racines réelles de polynômes trigonométriques aléatoires avec des coefficients i.i.d., qui sont soit bornés soit satisfont l’inégalité de Sobolev logarithmique, vérifie une concentration exponentielle de mesure.
Funding Statement
The first author is supported by National Science Foundation CAREER grant DMS-1752345.
The second author is partially supported by a US-Israel BSF grant.
This work was initiated when both authors visited the American Institute of Mathematics in August 2019. We thank AIM for its hospitality.
Acknowledgements
The authors are grateful to O. Nguyen and T. Erdély for help with references. They also thank the anonymous referees for helpful suggestions.
Citation
Hoi H. Nguyen. Ofer Zeitouni. "Exponential concentration for the number of roots of random trigonometric polynomials." Ann. Inst. H. Poincaré Probab. Statist. 60 (2) 1077 - 1089, May 2024. https://doi.org/10.1214/23-AIHP1366
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