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, ValentinaMembro 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.File | Dimensione | Formato | |
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