Random Waves On $\mathbb T^3$: Nodal Area Variance and Lattice Point Correlations

DOI10.1093/imrn/rnx220zbMath1443.11205arXiv1708.07015OpenAlexW2963453051MaRDI QIDQ5382544

Riccardo W. Maffucci, Jacques Benatar

Publication date: 18 June 2019

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.07015

zbMATH Keywords

Gaussian Laplace eigenfunctionslattice point correlations

Mathematics Subject Classification ID

Gaussian processes (60G15) Lattice points in specified regions (11P21)

Related Items (13)

On the variance of the nodal volume of arithmetic random waves ⋮ Random Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaos ⋮ Fluctuations of nodal sets on the 3-torus and general cancellation phenomena ⋮ Matrix Hermite polynomials, random determinants and the geometry of Gaussian fields ⋮ Asymptotic distribution of nodal intersections for ARW against a surface ⋮ Small scale CLTs for the nodal length of monochromatic waves ⋮ CENTRAL LIMIT THEOREM FOR PLANCK‐SCALE MASS DISTRIBUTION OF TORAL LAPLACE EIGENFUNCTIONS ⋮ Lattice points in \(d\)-dimensional spherical segments ⋮ Random nodal lengths and Wiener chaos ⋮ Gaussian random measures generated by Berry's nodal sets ⋮ Restriction of 3D arithmetic Laplace eigenfunctions to a plane ⋮ Nodal intersections for arithmetic random waves against a surface ⋮ On the correlation of critical points and angular trispectrum for random spherical harmonics

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