On the real zeros of random trigonometric polynomials with dependent coefficients

DOI10.1090/proc/14216zbMath1406.26007arXiv1706.01654OpenAlexW2964112851WikidataQ129188640 ScholiaQ129188640MaRDI QIDQ4555819

Federico Dalmao, Guillaume Poly, Jürgen Angst

Publication date: 23 November 2018

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.01654

zbMATH Keywords

asymptotic behaviorrandom coefficientstrigonometric polynomialsexpected number of real zeros

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Real polynomials: location of zeros (26C10) Trigonometric polynomials, inequalities, extremal problems (42A05)

Related Items (12)

Variance of the number of zeros of dependent Gaussian trigonometric polynomials ⋮ Real zeros of random cosine polynomials with palindromic blocks of coefficients ⋮ Real zeros of random trigonometric polynomials with dependent coefficients ⋮ Central limit theorem for the volume of the zero set of Kostlan-Shub-Smale random polynomial systems ⋮ Convergence in distribution norms in the CLT for non identical distributed random variables ⋮ How many roots of a system of random Laurent polynomials are real? ⋮ New asymptotics for the mean number of zeros of random trigonometric polynomials with strongly dependent Gaussian coefficients ⋮ Lipschitz-Killing curvatures for arithmetic random waves ⋮ Cumulants asymptotics for the zeros counting measure of real Gaussian processes ⋮ Real zeros of random trigonometric polynomials with $\ell$-periodic coefficients ⋮ Real zeros of random trigonometric polynomials with pairwise equal blocks of coefficients ⋮ On the correlation of critical points and angular trispectrum for random spherical harmonics

Uses Software

• longmemo

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