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2018 Eigenvectors of non normal random matrices
Florent Benaych-Georges, Ofer Zeitouni
Electron. Commun. Probab. 23: 1-12 (2018). DOI: 10.1214/18-ECP171

Abstract

We study the angles between the eigenvectors of a random $n\times n$ complex matrix $M$ with density $\propto \mathrm{e} ^{-n\operatorname{Tr} V(M^*M)}$ and $x\mapsto V(x^2)$ convex. We prove that for unit eigenvectors $\mathbf{v} ,\mathbf{v} '$ associated with distinct eigenvalues $\lambda ,\lambda '$ that are the closest to specified points $z,z'$ in the complex plane, the rescaled inner product \[ \sqrt{n} (\lambda '-\lambda )\langle \mathbf{v} ,\mathbf{v} '\rangle \] is uniformly sub-Gaussian, and give a more precise statement in the case of the Ginibre ensemble.

Citation

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Florent Benaych-Georges. Ofer Zeitouni. "Eigenvectors of non normal random matrices." Electron. Commun. Probab. 23 1 - 12, 2018. https://doi.org/10.1214/18-ECP171

Information

Received: 21 June 2018; Accepted: 25 September 2018; Published: 2018
First available in Project Euclid: 12 October 2018

zbMATH: 1403.15029
MathSciNet: MR3866043
Digital Object Identifier: 10.1214/18-ECP171

Subjects:
Primary: 15B52, 60B20

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