Local repulsion of planar Gaussian critical points

Safa Ladgham and Raphaël Lachieze-Rey

Stochastic Processes and their Applications, 2023, vol. 166, issue C

Abstract: We study the local repulsion between critical points of a stationary isotropic smooth planar Gaussian field. We show that the critical points can experience a soft repulsion which is maximal in the case of the random planar wave model, or a soft attraction of arbitrary high order. If the type of critical points is specified (extremum, saddle point), the points experience a hard local repulsion, that we quantify with the precise magnitude of the second factorial moment of the number of points in a small ball.

Keywords: Gaussian random fields; Stationary random fields; Critical points; Kac–Rice formula; Repulsive point process (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1016/j.spa.2023.09.008

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