Volume distribution of nodal domains of random band-limited functions

DOI10.1007/s00440-017-0813-xzbMath1404.60023arXiv1606.05766OpenAlexW2963306055WikidataQ58583089 ScholiaQ58583089MaRDI QIDQ1626609

Igor Wigman, Dmitri B. Beliaev

Publication date: 21 November 2018

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.05766

zbMATH Keywords

nodal domainsGaussian random fieldsrandom band-limited functions

Mathematics Subject Classification ID

Random fields (60G60) Geometric probability and stochastic geometry (60D05) Asymptotic distributions of eigenvalues in context of PDEs (35P20) Limit theorems in probability theory (60F99)

Related Items (12)

The expected nodal volume of non-Gaussian random band-limited functions, and their doubling index ⋮ No smooth phase transition for the nodal length of band-limited spherical random fields ⋮ Smoothness and monotonicity of the excursion set density of planar Gaussian fields ⋮ Small scale CLTs for the nodal length of monochromatic waves ⋮ Direction distribution for nodal components of random band-limited functions on surfaces ⋮ A covariance formula for topological events of smooth Gaussian fields ⋮ Mean conservation of nodal volume and connectivity measures for Gaussian ensembles ⋮ On the expected Betti numbers of the nodal set of random fields ⋮ Expected number of nodal components for cut‐off fractional Gaussian fields ⋮ Gaussian random measures generated by Berry's nodal sets ⋮ Limiting behavior for the excursion area of band-limited spherical random fields ⋮ Almost-sure asymptotics for Riemannian random waves

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