LOCAL REPULSION OF PLANAR GAUSSIAN CRITICAL POINTS

Safa Ladgham (1) , Raphaël Lachièze-Rey (1)

1 UPCité - Université Paris Cité

We study the local repulsion between critical points of a stationary isotropic smooth planar Gaussian field. We show that the critical points can experience a soft repulsion which is maximal in the case of the random planar wave model, or a soft attraction of arbitrary high order. If the type of critical points is specified (extremum, saddle point), the points experience a hard local repulsion, that we quantify with the precise magnitude of the second factorial moment of the number of points in a small ball.

Domaines: Probabilités [math.PR]

Safa Ladgham, Raphaël Lachièze-Rey. LOCAL REPULSION OF PLANAR GAUSSIAN CRITICAL POINTS. 2022. ⟨hal-03732460v1⟩