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Preprints, Working Papers, ... Year : 2022

LOCAL REPULSION OF PLANAR GAUSSIAN CRITICAL POINTS

Raphaël Lachièze-Rey

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.
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Dates and versions

hal-03732460 , version 1 (24-08-2022)
hal-03732460 , version 2 (08-09-2022)

Identifiers

  • HAL Id : hal-03732460 , version 1

Cite

Safa Ladgham, Raphaël Lachièze-Rey. LOCAL REPULSION OF PLANAR GAUSSIAN CRITICAL POINTS. 2022. ⟨hal-03732460v1⟩
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