Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators

Abstract

We consider quite general $h$-pseudodifferential operators on $R^n$ with small random perturbations and show that in the limit of small $h$ the eigenvalues are distributed according to a Weyl law with a probabality that tends to 1. The first author has previously obtained a similar result in dimension 1. Our class of perturbations is different.

This version contains improvements of the presentation and small corrections, in particular that of the power of $h$ in the smallness condition on delta in the main results