Description
It is now very well established that small random perturbations lead to probabilistic Weyl laws for the eigenvalue asymptotics of non-selfadjoint semiclassical pseudo-differential operators, Berezin-Toeplitz quantizations of compact Kähler manifolds and Toeplitz matrices. In this talk, I will I present recent work in collaboration with Anirban Basak and Ofer Zeitouni on eigenvector localization and delocalization in the model case of large non-selfadjoint Toeplitz matrices with small random perturbations.