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

## Authors

K. Truong

A. Ossipov

### 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.

### Citation

Truong, K., & Ossipov, A. (2016). Statistics of eigenvectors in the deformed Gaussian unitary ensemble of random matrices. Journal of Physics A: Mathematical and Theoretical, 49(14), https://doi.org/10.1088/1751-8113/49/14/145005

Journal Article Type Article Jan 25, 2016 Feb 23, 2016 Aug 4, 2017 Aug 4, 2017 Journal of Physics A: Mathematical and Theoretical 1751-8113 1751-8121 IOP Publishing Peer Reviewed 49 14 https://doi.org/10.1088/1751-8113/49/14/145005 http://eprints.nottingham.ac.uk/id/eprint/44637 http://iopscience.iop.org/article/10.1088/1751-8113/49/14/145005/meta Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf

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