# Repulsion or attraction of critical points of isotropic Gaussian fields.

We study the local behaviour of critical points of smooth Gaussian stationary and isotrope fields$R^N \to R$ . In dimension 1 ($N=1$) we deduce from well known results of the literature that there is always repulsion between critical points: they are better spread than a Poisson process. In higher dimension, depending on the dimension, we observe some neutrality when $N=2$ and attraction for $N>2$. Specifying the index of the critical points we give some interpretation. Our results generalise the result by Beliaev et al that concern the random plane wave.
• Repulsion or attraction of critical points of isotropic Gaussian fields.
• 2018-12-07T10:30:00-03:00
• 2018-12-07T11:30:00-03:00
• We study the local behaviour of critical points of smooth Gaussian stationary and isotrope fields$R^N \to R$ . In dimension 1 ($N=1$) we deduce from well known results of the literature that there is always repulsion between critical points: they are better spread than a Poisson process. In higher dimension, depending on the dimension, we observe some neutrality when $N=2$ and attraction for $N>2$. Specifying the index of the critical points we give some interpretation. Our results generalise the result by Beliaev et al that concern the random plane wave.
• When 07/12/2018 de 10:30 a 11:30 (America/Montevideo / UTC-300)
• Where Salón de Seminario - Centro de Matemática
• Contact
• Speaker Jean-Marc Azais
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