You are cordially invited to the Department of Mathematics Colloquium<\/p>\n
Speaker: Charles Bordenave (Institut de Math\u00e9matiques de Marseille and CNRS)<\/p>\n
“Random Perturbation of Toeplitz Matrices”<\/p>\n
Abstract: Toeplitz matrices form a rich and ubiquitous class of possibly non-normal matrices. Their asymptotic spectral analysis in high dimension is well-understood, as illustrated by the strong Szeg\u00f6 limit theorem for Toeplitz determinants. The spectra of these matrices are notoriously highly sensitive to small perturbations.
\nIn this talk, we explore the spectrum of a banded Toeplitz matrix perturbed by a random matrix in the asymptotic of high dimension. We show that the outlier eigenvalues are driven by a low-dimensional random analytic matrix field alongside an explicit deterministic matrix that captures the algebraic structure of the resonances responsible for the outlier eigenvalues. Along the way, we present new variations around the strong Szeg\u00f6 limit theorem. The talk is based on a joint work with Mireille Capitaine and Fran\u00e7ois Chapon.<\/p>\n
Charles Bordenave is Professor of Mathematics, Research Director at the CNRS, and a member of the Institut de Math\u00e9matiques de Marseille. Working at the interface of probability theory, random matrices, random graphs, and statistical physics, he has made major contributions to the study of large random structures and interacting particle systems. His work has appeared in leading journals such as Annals of Mathematics and Inventiones Mathematicae. He is the recipient of the Marc Yor Prize of the French Academy of Sciences and has been an IMS Medallion Lecturer. He has lectured at major institutions around the world, been a visiting scholar at the Institute for Advanced Study, and served on the editorial boards of leading journals in probability.<\/p>\n
Date: Wednesday, April 8, 2026
\nTime: 15:40-16:40
\nPlace: ZOOM and video conference in Mathematics Seminar Room, SA-141<\/p>\n
To request the event link, please contact gokhan.yildirim@bilkent.edu.tr<\/p>\n","protected":false},"excerpt":{"rendered":"
You are cordially invited to the Department of Mathematics Colloquium Speaker: Charles Bordenave (Institut de Math\u00e9matiques de Marseille and CNRS) “Random Perturbation of Toeplitz Matrices” Abstract: Toeplitz matrices form a rich and ubiquitous class of possibly non-normal matrices. Their asymptotic spectral analysis in high dimension is well-understood, as illustrated by [\u2026] <\/p>\n