A second moment bound for critical points of planar Gaussian fields in shrinking height windows

DOI10.1016/j.spl.2020.108698zbMath1447.60079arXiv1901.11336OpenAlexW3002623125WikidataQ126305550 ScholiaQ126305550MaRDI QIDQ2175599

Stephen Muirhead

Publication date: 29 April 2020

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.11336

zbMATH Keywords

critical pointsGaussian fieldssecond moment bound

Mathematics Subject Classification ID

Random fields (60G60) Limit theorems in probability theory (60F99)

Related Items (4)

Fluctuations of the number of excursion sets of planar Gaussian fields ⋮ Local repulsion of planar Gaussian critical points ⋮ On the expected Betti numbers of the nodal set of random fields ⋮ No repulsion between critical points for planar Gaussian random fields

Cites Work

• Number of critical points of a Gaussian random field: condition for a finite variance
• A central limit theorem for the Euler characteristic of a Gaussian excursion set
• On the second moment of the number of crossings by a stationary Gaussian process
• Fluctuations of the total number of critical points of random spherical harmonics
• Expected number and height distribution of critical points of smooth isotropic Gaussian random fields
• A CLT concerning critical points of random functions on a Euclidean space
• Nodal statistics of planar random waves
• Level Sets and Extrema of Random Processes and Fields
• On the Variance of the Number of Stationary Points of a Homogeneous Gaussian Field
• Regular and irregular semiclassical wavefunctions
• On the Variance of the Number of Zeros of a Stationary Gaussian Process

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