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

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 https://nottingham-repository.worktribe.com/output/775525 University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences https://doi.org/10.1088/1751-8113/49/14/145005 Ossipov, Alexander 04 Aug 2017 12:11 04 May 2020 17:35 http://eprints.nottingham.ac.uk/id/eprint/44637

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