Title: Perturbations of non-normal matrices
Abstract: Eigenvalues of Hermitian matrices are stable under perturbations in the sense that the $l_p$ norm of the difference between (ordered)eigenvalues is bounded by the Schatten norm of the perturbation. A similar control does not hold for non-Normal matrices. In the talk, I will discuss
perturbation by "vanishing noise" of large Toeplitz matrices with finitely supported symbols. In such cases, the empirical measure of eigenvalues converges to a measure which is the push forward of the uniform measure on $S^1$ by the symbol, when a (polynomialy) vanishing noise is applied. I will introduce the required notions,
explain why the above statement is true, and describe recent results concerning outliers.
Joint work(s) with Anirban Basak and Elliot Paquette