Almost sure Weyl asymptotics for non-self-adjoint elliptic operators on compact manifolds

TL;DR

This paper proves that for certain non-self-adjoint elliptic operators on compact manifolds, the distribution of large eigenvalues almost surely follows the classical Weyl law, extending known results from the self-adjoint case.

Contribution

It establishes almost sure Weyl asymptotics for non-self-adjoint elliptic operators with random perturbations, under weak assumptions.

Findings

Large eigenvalues follow Weyl law almost surely

Results extend Weyl asymptotics to non-self-adjoint operators

Applicable to operators with random 0th order perturbations

Abstract

In this paper, we consider elliptic differential operators on compact manifolds with a random perturbation in the 0th order term and show under fairly weak additional assumptions that the large eigenvalues almost surely distribute according to the Weyl law, well-known in the self-adjoint case.