Pseudospectra and eigenvalue asymptotics for disordered non-selfadjoint operators in the semiclassical limit

TL;DR

This paper reviews recent advances in understanding the pseudospectra and eigenvalue asymptotics of non-selfadjoint semiclassical pseudo-differential operators under small random perturbations, highlighting their spectral stability and asymptotic behavior.

Contribution

It synthesizes recent results on pseudospectra and eigenvalue asymptotics for disordered non-selfadjoint operators in the semiclassical limit.

Findings

Pseudospectra are significantly affected by small random perturbations.

Eigenvalue distributions exhibit specific asymptotic patterns in the semiclassical regime.

Random perturbations can stabilize spectral properties of non-selfadjoint operators.

Abstract

The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.