Dario Giandinoto: Asymptotic spectra for twisted Toeplitz matrices and their random perturbations

Abstract: Toeplitz matrices are matrices whose entries are constant on the diagonals; in twisted Toeplitz matrices the entries are slow-varying on the diagonals, rather than constant. In the first part of the talk, I will go over the classical results about the limiting spectral distribution for Toeplitz matrices and show some experiments regarding twisted Toeplitz matrices. In the second part, I will go over some more recent results about structured and unstructured random perturbations of Toeplitz matrices. One of these is the result of my joint work with my supervisor B. Shapiro.