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# On eigenvectors of perturbed Toeplitz matrices

## [HYBRID WORKSHOP] Connections and Introductory Workshop: Universality and Integrability in Random Matrix Theory and Interacting Particle Systems, Part 1 August 23, 2021 - August 27, 2021

August 23, 2021 (10:45 AM PDT - 11:45 AM PDT)
Speaker(s): Ofer Zeitouni (Weizmann Institute of Science)
Location: MSRI: Simons Auditorium, Online/Virtual
Tags/Keywords
• Eigenvector

• Toeplitz matrices

• pseudo-modes

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

#### On Eigenvectors Of Perturbed Toeplitz Matrices

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.

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