Outliers of Perturbations of Banded Toeplitz Matrices
Offered By: Institut des Hautes Etudes Scientifiques (IHES) via YouTube
Course Description
Overview
Explore the mathematical analysis of outlier eigenvalues in perturbed banded Toeplitz matrices through this 54-minute lecture. Delve into the study of matrices $M_n = T_n({\bf a}) + \sigma \frac{X_n}{\sqrt{n}}$, where $T_n({\bf a})$ is a Toeplitz matrix with symbol ${\bf a}$ and $X_n$ represents noise. Examine the convergence of the empirical spectral distribution as $n$ approaches infinity and investigate the behavior of eigenvalues in regions outside the support of the limiting measure. Gain insights into this collaborative research conducted by Mireille Capitaine, Charles Bordenave, and François Chapon at the Institut des Hautes Etudes Scientifiques (IHES).
Syllabus
Mireille Capitaine - Outliers of Perturbations of Banded Toeplitz Matrices
Taught by
Institut des Hautes Etudes Scientifiques (IHES)
Related Courses
Finding Low-Rank Matrices - From Matrix Completion to Recent TrendsSimons Institute via YouTube An Introduction to Determinantal Point Processes - John C Urschel
Institute for Advanced Study via YouTube Quantum Aspects of Black Holes - Lecture 3
International Centre for Theoretical Sciences via YouTube Quantum Phases of Matter - The SYK Model
International Centre for Theoretical Sciences via YouTube Fractionalized Metallic Phases in the Single Band Hubbard Model - Quantum Phases of Matter XXII
International Centre for Theoretical Sciences via YouTube