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2020 No repulsion between critical points for planar Gaussian random fields
Dmitry Beliaev, Valentina Cammarota, Igor Wigman
Electron. Commun. Probab. 25: 1-13 (2020). DOI: 10.1214/20-ECP362

Abstract

We study the behaviour of the point process of critical points of isotropic stationary Gaussian fields. We compute the main term in the asymptotic expansion of the two-point correlation function near the diagonal. Our main result implies that for a ‘generic’ field the critical points neither repel nor attract each other. Our analysis also allows to study how the short-range behaviour of critical points depends on their index.

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Dmitry Beliaev. Valentina Cammarota. Igor Wigman. "No repulsion between critical points for planar Gaussian random fields." Electron. Commun. Probab. 25 1 - 13, 2020. https://doi.org/10.1214/20-ECP362

Information

Received: 6 July 2020; Accepted: 12 November 2020; Published: 2020
First available in Project Euclid: 12 December 2020

Digital Object Identifier: 10.1214/20-ECP362

Subjects:
Primary: 58K05, 60G55, 60G60

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