Outliers of Perturbations of Banded Toeplitz Matrices

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).