Loi de Weyl presque sure pour un systeme differentiel en dimension 1

Abstract

We consider quite general differential operators on the circle with a small random lower order perturbation. We embrace two points a view, the semiclassical and the high energy limits. We show (a) in the semiclassical limit, that the eigenvalues inside a subdomain of the pseudospectrum are distributed according to a Weyl law with a probability close to 1, (b) that the large eigenvalues obey a Weyl law almost surely.