CLT for the zeros of classical random trigonometric polynomials

DOI10.1214/14-AIHP653zbMath1342.60025arXiv1401.5745OpenAlexW2964169404MaRDI QIDQ297456

Federico Dalmao, Jean-Marc Azaïs, José Rafael León

Publication date: 27 June 2016

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.5745

zbMATH Keywords

Gaussian processnumber of zeroscentral limit theoremWiener chaosrandom trigonometric polynomials

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Trigonometric polynomials, inequalities, extremal problems (42A05)

Related Items (13)

Variance of the number of zeros of dependent Gaussian trigonometric polynomials ⋮ On the real zeros of random trigonometric polynomials with dependent coefficients ⋮ Convergence in distribution norms in the CLT for non identical distributed random variables ⋮ A CLT concerning critical points of random functions on a Euclidean space ⋮ Winding number for stationary Gaussian processes using real variables ⋮ On the absolute continuity of random nodal volumes ⋮ Variance of real zeros of random orthogonal polynomials ⋮ Fluctuations for zeros of Gaussian Taylor series ⋮ Non universality for the variance of the number of real roots of random trigonometric polynomials ⋮ Random polynomials: central limit theorems for the real roots ⋮ Variations on Salem-Zygmund results for random trigonometric polynomials: application to almost sure nodal asymptotics ⋮ Variance of real zeros of random orthogonal polynomials for varying and exponential weights ⋮ Nodal deficiency of random spherical harmonics in presence of boundary

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