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.

No repulsion between critical points for planar Gaussian random fields / Beliaev, Dmitry; Cammarota, Valentina; Wigman, Igor. - In: ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X. - 25:(2020). [10.1214/20-ECP362]

No repulsion between critical points for planar Gaussian random fields

Cammarota, Valentina
Membro del Collaboration Group
;
2020

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.
2020
gaussian fields; critical points
01 Pubblicazione su rivista::01a Articolo in rivista
No repulsion between critical points for planar Gaussian random fields / Beliaev, Dmitry; Cammarota, Valentina; Wigman, Igor. - In: ELECTRONIC COMMUNICATIONS IN PROBABILITY. - ISSN 1083-589X. - 25:(2020). [10.1214/20-ECP362]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1466982
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