On toral eigenfunctions and the random wave model

DOI10.1007/s11856-014-1037-zzbMath1305.60013arXiv1303.2881OpenAlexW2591747415MaRDI QIDQ466094

Jean Bourgain

Publication date: 24 October 2014

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.2881

zbMATH Keywords

two-dimensional torusdeterministic implementationrandom wave model

Mathematics Subject Classification ID

Probability theory on algebraic and topological structures (60B99)

Related Items (21)

On the variance of the nodal volume of arithmetic random waves ⋮ Concentration of the number of intersections of random eigenfunctions on flat tori ⋮ Nodal set of monochromatic waves satisfying the random wave model ⋮ On the number of nodal domains of toral eigenfunctions ⋮ The expected nodal volume of non-Gaussian random band-limited functions, and their doubling index ⋮ Planck-scale number of nodal domains for toral eigenfunctions ⋮ Asymptotic nodal length and log-integrability of toral eigenfunctions ⋮ On the universality of the Nazarov-Sodin constant ⋮ Eigenvectors of the square grid plus GUE ⋮ Fluctuations in Salem-Zygmund almost sure central limit theorem ⋮ Bounding the number of nodal domains of eigenfunctions without singular points on the square ⋮ CENTRAL LIMIT THEOREM FOR PLANCK‐SCALE MASS DISTRIBUTION OF TORAL LAPLACE EIGENFUNCTIONS ⋮ Planck-scale distribution of nodal length of arithmetic random waves ⋮ On the distribution of local extrema in quantum chaos ⋮ Local weak limits of Laplace eigenfunctions ⋮ How Lagrangian states evolve into random waves ⋮ Variations on Salem-Zygmund results for random trigonometric polynomials: application to almost sure nodal asymptotics ⋮ Nodal deficiency of random spherical harmonics in presence of boundary ⋮ The defect of toral Laplace eigenfunctions and arithmetic random waves ⋮ Unnamed Item ⋮ Almost-sure asymptotics for Riemannian random waves

Cites Work

• Unnamed Item
• Nodal domains of Maass forms. I
• On the angular distribution of Gaussian integers with fixed norm
• Linear equations in variables which lie in a multiplicative group
• On the number of nodal domains of random spherical harmonics
• On the mininum number of domains in which the nodal lines of spherical harmonics divide the sphere
• Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature
• On Pleijel's Nodal Domain Theorem
• A Problem on Sums of Two Squares
• Random wavefunctions and percolation
• Lattice points on circles and discrete velocity models for the Boltzmann equation

This page was built for publication: On toral eigenfunctions and the random wave model