Uniform individual asymptotics for the eigenvalues and eigenvectors of large Toeplitz matrices

Cupples I Room 215

The asymptotic behavior of the spectrum of large Toeplitz matrices has been studied for almost one century now. Among this huge work, we can nd the Szeg\H{o} theorems on the eigenvalue distribution and the asymptotics for the determinants, as well as other theorems about the individual asymptotics for the smallest and largest eigenvalues. Results about uniform individual asymptotics for all the eigenvalues and eigenvectors appeared only ve years ago. The goal of the present lecture is to review this area, to talk about the obtained results. This review is based on joint works with Manuel Bogoya, Albrecht B\"ottcher, and Egor Maximenko.