Local repulsion of planar Gaussian critical points
Probability
2022-09-12 v1
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
Cite
@article{arxiv.2209.04150,
title = {Local repulsion of planar Gaussian critical points},
author = {Safa Ladgham and Raphaël Lachièze-Rey},
journal= {arXiv preprint arXiv:2209.04150},
year = {2022}
}