Eigenvalue interaction for a class of nonselfadjoint operators under random perturbations

Orateur: VOGEL Martin
Localisation: Université de Dijon, France
Type: Séminaire problèmes spectraux en physique mathématique
Site: IHP
Salle: 314
Date de début: 20/10/2014 - 14:00
Date de fin: 20/10/2014 - 14:00

We consider a nonselfadjoint $h$-differential model operator $P_h$ in the semiclassical limit, subject to small random perturbations. We study the $2$-point intensity measure of the random point process of eigenvalues of the randomly perturbed operator $P_h$ and give an $h$-asymptotic formula for the average $2$-point density of eigenvalues, avoiding two eigenvalues being closer than $h^{3/5}$. With this formula we show that any two eigenvalues of $P_h$ lying in the interior of the classical spectrum (the range of the principal symbol of $P_h$) exhibit close range repulsion and long range decoupling.