Two Point Function for Critical Points of a Random Plane Wave

DOI10.1093/imrn/rnx197zbMath1429.58038arXiv1704.04943OpenAlexW2963316810MaRDI QIDQ5243356

Igor Wigman, Valentina Cammarota, Dmitri B. Beliaev

Publication date: 18 November 2019

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.04943

zbMATH Keywords

Laplace operatorcritical pointsrandom plane wavehigh-energy eigenfunctions

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Harmonic maps, etc. (58E20)

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Superposition of random plane waves in high spatial dimensions: Random matrix approach to landscape complexity ⋮ Mean number and correlation function of critical points of isotropic Gaussian fields and some results on GOE random matrices ⋮ Random Lipschitz–Killing curvatures: Reduction Principles, Integration by Parts and Wiener chaos ⋮ Functional convergence of Berry's nodal lengths: approximate tightness and total disorder ⋮ Local repulsion of planar Gaussian critical points ⋮ Critical point asymptotics for Gaussian random waves with densities of any Sobolev regularity ⋮ Effective bounds for monochromatic connectivity measures in two dimensions ⋮ Unnamed Item ⋮ Gaussian random measures generated by Berry's nodal sets ⋮ No repulsion between critical points for planar Gaussian random fields

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