Statistical properties of eigenvectors and eigenvalues of structured random matrices

Truong, K. and Ossipov, A. (2018) Statistical properties of eigenvectors and eigenvalues of structured random matrices. Journal of Physics A: Mathematical and Theoretical, 51 (6). 065001/1-065001/12. ISSN 1751-8121

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Abstract

We study the eigenvalues and the eigenvectors of N X N structured random matrices of the form H = W ~HW+D with diagonal matrices D and W and ~H from the Gaussian Unitary Ensemble. Using the supersymmetry technique we derive general asymptotic expressions for the density of states and the moments of the eigenvectors. We find that the eigenvectors remain ergodic under very general assumptions, but a degree of their ergodicity depends strongly on a particular choice of W and D. For a special case of D = 0 and random W, we show that the eigenvectors can become critical and are characterized by non-trivial fractal dimensions.

Item Type: Article
Additional Information: “This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1751-8121/aaa011
Keywords: Random matrix theory; Statistics of eigenvectors; Localization
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1088/1751-8121/aaa011
Depositing User: Ossipov, Alexander
Date Deposited: 12 Jan 2018 09:47
Last Modified: 13 Jan 2018 12:11
URI: http://eprints.nottingham.ac.uk/id/eprint/49036

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