Local universality for real roots of random trigonometric polynomials

DOI10.1214/16-EJP9zbMath1361.30009arXiv1601.05740OpenAlexW2963161108MaRDI QIDQ728436

Zakhar Kabluchko, Alexander Marynych, Aleksander M. Iksanov

Publication date: 20 December 2016

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.05740

zbMATH Keywords

real zerosrandom trigonometric polynomials

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) Functional limit theorems; invariance principles (60F17)

Related Items (14)

Real zeros of random trigonometric polynomials with dependent coefficients ⋮ On the real zeros of random trigonometric polynomials with dependent coefficients ⋮ Random trigonometric polynomials: universality and non-universality of the variance for the number of real roots ⋮ New asymptotics for the mean number of zeros of random trigonometric polynomials with strongly dependent Gaussian coefficients ⋮ Limit theorems for random Dirichlet series ⋮ Rates of convergence for the number of zeros of random trigonometric polynomials ⋮ Fluctuations in Salem-Zygmund almost sure central limit theorem ⋮ Universality of the minimum modulus for random trigonometric polynomials ⋮ Expected number of real zeroes of random Taylor series ⋮ Universality of the nodal length of bivariate random trigonometric polynomials ⋮ Real zeroes of random analytic functions associated with geometries of constant curvature ⋮ Non universality for the variance of the number of real roots of random trigonometric polynomials ⋮ Variations on Salem-Zygmund results for random trigonometric polynomials: application to almost sure nodal asymptotics ⋮ Roots of random functions: A framework for local universality

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