The defect of toral Laplace eigenfunctions and arithmetic random waves

DOI10.1088/1361-6544/ac17c8zbMath1471.58012arXiv2006.11644OpenAlexW3036024038MaRDI QIDQ5010062

Pär Kurlberg, Nadav Yesha, Igor Wigman

Publication date: 24 August 2021

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.11644

zbMATH Keywords

signed measure Gaussian probability measure standard torus Laplace eigenfunctions defect distribution

Mathematics Subject Classification ID

Gaussian processes (60G15) Probability distributions: general theory (60E05) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (3)

Random Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaos ⋮ Lipschitz-Killing curvatures for arithmetic random waves ⋮ Some recent developments on the geometry of random spherical eigenfunctions

Cites Work

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On the number of nodal domains of toral eigenfunctions
On toral eigenfunctions and the random wave model
On probability measures arising from lattice points on circles
The distribution of the lattice points on circles
On the angular distribution of Gaussian integers with fixed norm
Equidistribution in shrinking sets and \(L^4\)-norm bounds for automorphic forms
Nodal length fluctuations for arithmetic random waves
Planck-scale distribution of nodal length of arithmetic random waves
Planck-scale mass equidistribution of toral Laplace eigenfunctions
On nonlinear functionals of random spherical eigenfunctions
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
Simultaneous approximation to algebraic numbers by rationals
Asymptotic Laws for the Spatial Distribution and the Number of Connected Components of Zero Sets of Gaussian Random Functions
Topologies of Nodal Sets of Random Band‐Limited Functions
The defect variance of random spherical harmonics
Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature
On the fractal structure of attainable probability measures
Mass distribution for toral eigenfunctions via Bourgain’s de-randomization
A Problem on Sums of Two Squares
CENTRAL LIMIT THEOREM FOR PLANCK‐SCALE MASS DISTRIBUTION OF TORAL LAPLACE EIGENFUNCTIONS
Lattice points on circles and discrete velocity models for the Boltzmann equation
Sign and area in nodal geometry of Laplace eigenfunctions
Mathematical Analysis of Random Noise
Mathematical Analysis of Random Noise

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