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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: SLMath: Eisenbud 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.

Supplements
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Video/Audio Files

On Eigenvectors Of Perturbed Toeplitz Matrices

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