### Videos

#### On eigenvectors of perturbed Toeplitz matrices

##### Presenter
August 23, 2021
Keywords:
• Eigenvector
• Toeplitz matrices
• pseudo-modes
MSC:
• 60B20
• 15B52
##### Abstract
We consider Toeplitz matrices perturbed by vanishing noise, i.e. noise of the form $N^{-\gamma} G$ with $\gamma>1/2$ and $G$ having iid zero mean entries of variance $1$; the resulting spectrum concentrates around spectral curves determined by the symbol. For $\gamma>1$, we prove localization of eigenvectors and show they are close to certain pseudo-modes. I will also discuss the case $\gamma\in (1/2,1)$, where a different behavior emerges. Joint work with Anirban Basak and Martin Vogel.