On the number of nodal domains of random spherical harmonics

From MaRDI portal
Publication:3644286

DOI10.1353/ajm.0.0070zbMath1186.60022arXiv0706.2409OpenAlexW2082444183MaRDI QIDQ3644286

Mikhail Sodin, F. L. Nazarov

Publication date: 3 November 2009

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

Full work available at URL: https://arxiv.org/abs/0706.2409




Related Items

A quantitative central limit theorem for the Euler-Poincaré characteristic of random spherical eigenfunctionsConcentration of the number of intersections of random eigenfunctions on flat toriVolume distribution of nodal domains of random band-limited functionsEquidistribution of the conormal cycle of random nodal setsFluctuations of the number of excursion sets of planar Gaussian fieldsOn the geometry of random lemniscatesTopological properties of Neumann domainsWeighted local Weyl laws for elliptic operatorsVariation of the Nazarov-Sodin constant for random plane waves and arithmetic random wavesUniversal components of random nodal setsNodal set of monochromatic waves satisfying the random wave modelEXPECTED TOPOLOGY OF RANDOM REAL ALGEBRAIC SUBMANIFOLDSOn the number of nodal domains of toral eigenfunctionsOn the distribution of the critical values of random spherical harmonicsOn the correlation between critical points and critical values for random spherical harmonicsAsymptotic topology of excursion and nodal sets of Gaussian random fieldsHole probability for nodal sets of the cut-off Gaussian free fieldPoints on nodal lines with given directionNodal statistics on quantum graphsNodal domains of Maass forms. IFluctuations of the total number of critical points of random spherical harmonicsStationary phase methods and the splitting of separatricesEquality of critical parameters for percolation of Gaussian free field level setsThe expected nodal volume of non-Gaussian random band-limited functions, and their doubling indexThe Gauss-Bonnet-Chern theorem: A probabilistic perspectiveLipschitz-Killing curvatures for arithmetic random wavesSome recent developments on the geometry of random spherical eigenfunctionsBeltrami fields exhibit knots and chaos almost surelyUniversality: random matrices, random geometry and SPDEs. Abstracts from the workshop held May 29 -- June 4, 2022On the universality of the Nazarov-Sodin constantLimit cycle enumeration in random vector fieldsThe phase transition for planar Gaussian percolation models without FKGSharp phase transition for Gaussian percolation in all dimensionsSystoles and Lagrangians of random complex algebraic hypersurfacesDynamics of nodal points and the nodal count on a family of quantum graphsSmooth Gaussian fields and percolationCritical point asymptotics for Gaussian random waves with densities of any Sobolev regularitySpherical Poisson wavesNo smooth phase transition for the nodal length of band-limited spherical random fieldsBounding the number of nodal domains of eigenfunctions without singular points on the squareNodal length fluctuations for arithmetic random wavesLow-degree approximation of random polynomialsExponential rarefaction of real curves with many componentsOn the number of excursion sets of planar Gaussian fieldsDirection distribution for nodal components of random band-limited functions on surfacesMean conservation of nodal volume and connectivity measures for Gaussian ensemblesOn toral eigenfunctions and the random wave modelOn nonlinear functionals of random spherical eigenfunctionsTangent nodal sets for random spherical harmonicsOn the number of connected components of random algebraic hypersurfacesThe minimum numbers of nodal domains of spherical Grushin-harmonicsEffective bounds for monochromatic connectivity measures in two dimensionsA reduction principle for the critical values of random spherical harmonicsPercolation of random nodal linesDiscretisation schemes for level sets of planar Gaussian fieldsRestriction of toral eigenfunctions to hypersurfaces and nodal setsA. Stern's analysis of the nodal sets of some families of spherical harmonics revisitedNon-universality of the Nazarov-Sodin constantSup-norm and nodal domains of dihedral Maass formsOn Spectral Minimal Partitions: the Case of the SphereThe lemniscate tree of a random polynomialQuantitative quantum ergodicity and the nodal domains of Hecke-Maass cusp formsLocal weak limits of Laplace eigenfunctionsExpected number of nodal components for cut‐off fractional Gaussian fieldsFluctuations in the number of nodal domainsPersistence barcodes and Laplace eigenfunctions on surfacesNo repulsion between critical points for planar Gaussian random fieldsReal lines on random cubic surfacesLimiting behavior for the excursion area of band-limited spherical random fieldsThe defect of random hyperspherical harmonicsVariance of the volume of random real algebraic submanifoldsQuasi-independence for nodal linesRandom matrices and the average topology of the intersection of two quadricsUnnamed ItemLower estimates for the expected Betti numbers of random real hypersurfacesArithmetic, zeros, and nodal domains on the sphereKac-Rice formula for transverse intersectionsGap probabilities and Betti numbers of a random intersection of quadrics