No repulsion between critical points for planar Gaussian random fields
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.