Nodal intersections for random waves on the 3-dimensional torus

DOI10.5802/aif.3068zbMath1360.60081arXiv1501.07410OpenAlexW2963919113MaRDI QIDQ506596

Nadav Yesha, Igor Wigman, Ze'ev Rudnick

Publication date: 1 February 2017

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.07410

zbMATH Keywords

asymptoticscurvaturetorusvariancenodal lineintersection pointsrandom Gaussian Laplace eigenfunctionstest curve

Mathematics Subject Classification ID

Gaussian processes (60G15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Lattice points in specified regions (11P21)

Related Items (18)

Nodal intersections of random eigenfunctions against a segment on the 2-dimensional torus ⋮ Concentration of the number of intersections of random eigenfunctions on flat tori ⋮ On the correlation between critical points and critical values for random spherical harmonics ⋮ Random Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaos ⋮ Fluctuations of nodal sets on the 3-torus and general cancellation phenomena ⋮ Asymptotic distribution of nodal intersections for arithmetic random waves ⋮ Invariant Gaussian fields on homogeneous spaces: explicit constructions and mean nodal volume ⋮ Lipschitz-Killing curvatures for arithmetic random waves ⋮ Some recent developments on the geometry of random spherical eigenfunctions ⋮ Asymptotic distribution of nodal intersections for ARW against a surface ⋮ A quantitative central limit theorem for the excursion area of random spherical harmonics over subdomains of S2 ⋮ Random nodal lengths and Wiener chaos ⋮ A reduction principle for the critical values of random spherical harmonics ⋮ Nodal intersections for random waves against a segment on the 3-dimensional torus ⋮ Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics ⋮ 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

Cites Work

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• Nodal length fluctuations for arithmetic random waves
• Nodal intersections and \(L^p\) restriction theorems on the torus
• On the volume of nodal sets for eigenfunctions of the Laplacian on the torus
• Fluctuations of the Euler-Poincaré characteristic for random spherical harmonics
• Nodal intersections for random eigenfunctions on the torus
• Level Sets and Extrema of Random Processes and Fields

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