Repulsion of zeros of Gaussian fields
vendredi 2 juillet 2021, 16h00 - 17h00
We are interested in the study of the local repulsion of the zeros of smooth stationary planar Gaussian fields from ℝ² to ℝ. The study is deepened by analyzing separately the different types of critical points: local minima, local maxima, saddle, extrema. In a first part we study the expectation of the number of critical points.
In a second part we study the asymptotic behaviour of the second factorial moment of the number of critical points in the disc ℬ(ρ) when ρ goes to zero. Our main result implies that we have a stronger repulsion between extremal points.