On the volume of nodal sets for eigenfunctions of the Laplacian on the torus

From MaRDI portal
Publication:2478160

DOI10.1007/s00023-007-0352-6zbMath1142.60029arXivmath-ph/0702081OpenAlexW3103979390MaRDI QIDQ2478160

Igor Wigman, Ze'ev Rudnick

Publication date: 14 March 2008

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0702081




Related Items (49)

On the variance of the nodal volume of arithmetic random wavesEquidistribution of the conormal cycle of random nodal setsNon-universality of nodal length distribution for arithmetic random wavesVariation of the Nazarov-Sodin constant for random plane waves and arithmetic random wavesRandom Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaosPoints on nodal lines with given directionThe asymptotic equivalence of the sample trispectrum and the nodal length for random spherical harmonicsFluctuations of nodal sets on the 3-torus and general cancellation phenomenaRemarks on nodal volume statistics for regular and chaotic wave functions in various dimensionsAsymptotic distribution of nodal intersections for arithmetic random wavesBoundary effect on the nodal length for arithmetic random waves, and spectral semi-correlationsInvariant Gaussian fields on homogeneous spaces: explicit constructions and mean nodal volumeThe expected nodal volume of non-Gaussian random band-limited functions, and their doubling indexLipschitz-Killing curvatures for arithmetic random wavesSome recent developments on the geometry of random spherical eigenfunctionsNodal statistics of planar random wavesAsymptotic nodal length and log-integrability of toral eigenfunctionsFluctuations of the nodal length of random spherical harmonicsSpherical Poisson wavesMatrix Hermite polynomials, random determinants and the geometry of Gaussian fieldsLocal universality for zeros and critical points of monochromatic random wavesAsymptotic distribution of nodal intersections for ARW against a surfaceNodal length fluctuations for arithmetic random wavesNodal lengths in shrinking domains for random eigenfunctions on \(S^2\)Universal statistics of vortex tangles in three-dimensional random wavesSmall scale CLTs for the nodal length of monochromatic wavesMetric properties in the mean of polynomials on compact isotropy irreducible homogeneous spacesRandom nodal lengths and Wiener chaosNodal intersections for random waves on the 3-dimensional torusPlanck-scale distribution of nodal length of arithmetic random wavesNodal intersections for random waves against a segment on the 3-dimensional torusThe Leray measure of nodal sets for random eigenfunctions on the torusUniversality of the nodal length of bivariate random trigonometric polynomialsSome remarks on spherical harmonicsUnnamed ItemMonochromatic Random Waves for General Riemannian ManifoldsGaussian random measures generated by Berry's nodal setsCritical points of multidimensional random Fourier series: Variance estimatesNodal area distribution for arithmetic random wavesPhase singularities in complex arithmetic random wavesOn the distribution of the nodal sets of random spherical harmonicsRestriction of 3D arithmetic Laplace eigenfunctions to a planeThe defect of random hyperspherical harmonicsNodal intersections for arithmetic random waves against a surfaceVariance of the volume of random real algebraic submanifoldsNodal deficiency of random spherical harmonics in presence of boundaryThe defect of toral Laplace eigenfunctions and arithmetic random wavesAlmost-sure asymptotics for Riemannian random wavesExpected volume and Euler characteristic of random submanifolds




This page was built for publication: On the volume of nodal sets for eigenfunctions of the Laplacian on the torus