Statistical properties of eigenvectors and eigenvalues of structured random matrices
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...
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| Format: | Article |
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IOP
2018
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| Online Access: | https://eprints.nottingham.ac.uk/49036/ |
| _version_ | 1848797908981252096 |
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| author | Truong, K. Ossipov, A. |
| author_facet | Truong, K. Ossipov, A. |
| author_sort | Truong, K. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T20:11:21Z |
| format | Article |
| id | nottingham-49036 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:11:21Z |
| publishDate | 2018 |
| publisher | IOP |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-490362020-05-04T19:26:33Z https://eprints.nottingham.ac.uk/49036/ Statistical properties of eigenvectors and eigenvalues of structured random matrices Truong, K. Ossipov, A. 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. IOP 2018-01-10 Article PeerReviewed 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 Random matrix theory; Statistics of eigenvectors; Localization https://doi.org/10.1088/1751-8121/aaa011 doi:10.1088/1751-8121/aaa011 doi:10.1088/1751-8121/aaa011 |
| spellingShingle | Random matrix theory; Statistics of eigenvectors; Localization Truong, K. Ossipov, A. Statistical properties of eigenvectors and eigenvalues of structured random matrices |
| title | Statistical properties of eigenvectors and eigenvalues of structured random matrices |
| title_full | Statistical properties of eigenvectors and eigenvalues of structured random matrices |
| title_fullStr | Statistical properties of eigenvectors and eigenvalues of structured random matrices |
| title_full_unstemmed | Statistical properties of eigenvectors and eigenvalues of structured random matrices |
| title_short | Statistical properties of eigenvectors and eigenvalues of structured random matrices |
| title_sort | statistical properties of eigenvectors and eigenvalues of structured random matrices |
| topic | Random matrix theory; Statistics of eigenvectors; Localization |
| url | https://eprints.nottingham.ac.uk/49036/ https://eprints.nottingham.ac.uk/49036/ https://eprints.nottingham.ac.uk/49036/ |