Ricerc@Sapienza

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.