Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices

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Truong, K. and Ossipov, A. (2016) Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices. Journal of Physics A: Mathematical and Theoretical, 49 (14). p. 145005. ISSN 1751-8121

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Abstract

We study eigenvectors in the deformed Gaussian unitary ensemble of random matrices $H=W\tilde{H}W$, where $\tilde{H}$ is a random matrix from the Gaussian unitary ensemble and W is a deterministic diagonal matrix with positive entries. Using the supersymmetry approach we calculate analytically the moments and the distribution function of the eigenvectors components for a generic matrix W. We show that specific choices of W can modify significantly the nature of the eigenvectors changing them from extended to critical to localized. Our analytical results are supported by numerical simulations.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/775525
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1088/1751-8113/49/14/145005
Depositing User: Ossipov, Alexander
Date Deposited: 04 Aug 2017 12:11
Last Modified: 04 May 2020 17:35
URI: https://eprints.nottingham.ac.uk/id/eprint/44637

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