Valentina Cammarota (Roma La Sapienza)

Two Point Function for Critical Points of a Random Plane Wave

vendredi 20 avril 2018, 9h30 - 10h30

Salle du conseil, espace Turing

Random plane wave is conjectured to be a universal model for high-energy eigenfunctions of the Laplace operator on generic compact Riemannian manifolds. This is known to be true on average. We will discuss one of important geometric observable: critical points. We first compute one-point function for the critical point process, in particular we compute the expected number of critical points inside any open set. After that we compute the short-range asymptotic behaviour of the two-point function. This gives an unexpected result that the second factorial moment of the number of critical points in a small disc scales as the fourth power of the radius. Based on a joint work with Dmitry Beliaev and Igor Wigman