Modul: MAT971 Stochastische Prozesse

## Random perturbations of non-Normal matrices

Prof. Dr. Ofer Zeitouni talk

Speaker invited by: Prof. Dr. Erwin Bolthausen

**Date:** 04.03.20 **Time:** 17.15 - 19.00 **Room:** Y27H12

Non-normal matrices can exhibit a high sensitivity to perturbations, as the case of a matrix with a single block in its Jordan decomposition shows. Yet, when randomly perturbed, the spectrum of such matrices exhibits a remarkable stability. For example, the spectrum of randomly perturbed non-Hermitian Toeplitz matrices concentrates on certain spectral curves, that are typically outside the spectrum of the unperturbed operator. Further, the outliers process (away from the spectral curve) turns out to have interesting characteristics.

I will discuss these developments. Based on joint works with Anirban Basak, Elliot Paquette, and Martin Vogel.