Non universality for the variance of the number of real roots of random trigonometric polynomials

DOI10.1007/s00440-018-0869-2zbMath1478.60136arXiv1711.03316OpenAlexW2963248156WikidataQ129207136 ScholiaQ129207136MaRDI QIDQ2312683

Vlad Bally, Guillaume Poly, Lucia Caramellino

Publication date: 17 July 2019

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.03316

zbMATH Keywords

Kac-Rice formularandom trigonometric polynomialssmall balls estimatesEdgeworth expansion for non smooth functions

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50)

Related Items (12)

Variance of the number of zeros of dependent Gaussian trigonometric polynomials ⋮ Random trigonometric polynomials: universality and non-universality of the variance for the number of real roots ⋮ The expected nodal volume of non-Gaussian random band-limited functions, and their doubling index ⋮ Lipschitz-Killing curvatures for arithmetic random waves ⋮ Some recent developments on the geometry of random spherical eigenfunctions ⋮ Convergence in total variation for nonlinear functionals of random hyperspherical harmonics ⋮ Fluctuations in Salem-Zygmund almost sure central limit theorem ⋮ Universality of the minimum modulus for random trigonometric polynomials ⋮ Fluctuations for zeros of Gaussian Taylor series ⋮ Variations on Salem-Zygmund results for random trigonometric polynomials: application to almost sure nodal asymptotics ⋮ Regularization lemmas and convergence in total variation ⋮ On the correlation of critical points and angular trispectrum for random spherical harmonics

Cites Work

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• On the Expected Number of Real Zeros of Random Polynomials I. Coefficients with Zero Means
• Universality of the nodal length of bivariate random trigonometric polynomials
• Local Universality of Zeroes of Random Polynomials
• On the Average Number of Real Roots of a Random Algebraic Equation (II)
• Random Eigenfunctions on Flat Tori: Universality for the Number of Intersections

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