Points on nodal lines with given direction

DOI10.4171/JST/317zbMath1472.58020arXiv1802.09603OpenAlexW2976440373MaRDI QIDQ2662230

Igor Wigman, Ze'ev Rudnick

Publication date: 9 April 2021

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.09603

zbMATH Keywords

nodal linearithmetic random wavestoral Laplace eigenfunctionsgradient directionzero set.

Mathematics Subject Classification ID

Random fields (60G60) Gaussian processes (60G15) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Sample path properties (60G17) Diffusion processes and stochastic analysis on manifolds (58J65) Geodesics in global differential geometry (53C22) Real polynomials: location of zeros (26C10)

Related Items (2)

Direction distribution for nodal components of random band-limited functions on surfaces ⋮ Tangent nodal sets for random spherical harmonics

Cites Work

• Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
• Non-universality of nodal length distribution for arithmetic random waves
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• Quantitative limit theorems for local functionals of arithmetic random waves
• Nodal length fluctuations for arithmetic random waves
• 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
• Asymptotic Laws for the Spatial Distribution and the Number of Connected Components of Zero Sets of Gaussian Random Functions
• EXPECTED TOPOLOGY OF RANDOM REAL ALGEBRAIC SUBMANIFOLDS
• Level Sets and Extrema of Random Processes and Fields
• On the number of nodal domains of random spherical harmonics
• Lower Bounds for the Zeros of Bessel Functions
• The Number of Nodal Components of Arithmetic Random Waves
• Nodal Sets of Laplace Eigenfunctions: Estimates of the Hausdorff Measure in Dimensions Two and Three
• On Pleijel's Nodal Domain Theorem

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