Universality of the nodal length of bivariate random trigonometric polynomials

DOI10.1090/tran/7255zbMath1407.42001arXiv1610.05360OpenAlexW2537110098MaRDI QIDQ4691075

Viet-Hung Pham, Jürgen Angst, Guillaume Poly

Publication date: 18 October 2018

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

Full work available at URL: https://arxiv.org/abs/1610.05360

zbMATH Keywords

Poincaré formulaKac-Rice formulaGaussian fieldnodal length

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) Real polynomials: location of zeros (26C10) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Trigonometric polynomials, inequalities, extremal problems (42A05)

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Cites Work

• Unnamed Item
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• Expected volume and Euler characteristic of random submanifolds
• Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
• Non-universality of nodal length distribution for arithmetic random waves
• On the number of connected components of random algebraic hypersurfaces
• Small ball estimates for quasi-norms
• Fluctuations of the nodal length of random spherical harmonics
• Local universality for real roots of random trigonometric polynomials
• Distribution of zeros of random and quantum chaotic sections of positive line bundles
• Expected number of real roots of random trigonometric polynomials
• On the volume of nodal sets for eigenfunctions of the Laplacian on the torus
• The Leray measure of nodal sets for random eigenfunctions on the torus
• Random Complex Zeroes and Random Nodal Lines
• Mean Number of Real Zeros of a Random Trigonometric Polynomial
• Level Sets and Extrema of Random Processes and Fields
• On the Expected Number of Real Zeros of Random Polynomials I. Coefficients with Zero Means
• Local Universality of Zeroes of Random Polynomials