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Article: Universality for a global property of the eigenvectors of Wigner matrices
| Title | Universality for a global property of the eigenvectors of Wigner matrices |
|---|---|
| Authors | |
| Issue Date | 2014 |
| Citation | Journal of Mathematical Physics, 2014, v. 55, n. 2, article no. 023303 How to Cite? |
| Abstract | Let Mn be an n×n real (resp. complex) Wigner matrix and UnΔnU*n be its spectral decomposition. Set (y1, y2 ..., yn)T = U*n x, where x = (x1, x2, xn)T is a real (resp. complex) unit vector. Under the assumption that the elements of Mn have 4 matching moments with those of GOE (resp. GUE), we show that the process converges weakly to the Brownian bridge for any x satisfying x∞ → 0 as n → 8, where β = 1 for the real case and β = 2 for the complex case. Such a result indicates that the orthogonal (resp. unitary) matrices with columns being the eigenvectors of Wigner matrices are asymptotically Haar distributed on the orthogonal (resp. unitary) group from a certain perspective. © 2014 AIP Publishing LLC. |
| Persistent Identifier | http://hdl.handle.net/10722/349038 |
| ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 0.569 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Bao, Zhigang | - |
| dc.contributor.author | Pan, Guangming | - |
| dc.contributor.author | Zhou, Wang | - |
| dc.date.accessioned | 2024-10-17T06:55:51Z | - |
| dc.date.available | 2024-10-17T06:55:51Z | - |
| dc.date.issued | 2014 | - |
| dc.identifier.citation | Journal of Mathematical Physics, 2014, v. 55, n. 2, article no. 023303 | - |
| dc.identifier.issn | 0022-2488 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/349038 | - |
| dc.description.abstract | Let Mn be an n×n real (resp. complex) Wigner matrix and UnΔnU*n be its spectral decomposition. Set (y1, y2 ..., yn)T = U*n x, where x = (x1, x2, xn)T is a real (resp. complex) unit vector. Under the assumption that the elements of Mn have 4 matching moments with those of GOE (resp. GUE), we show that the process converges weakly to the Brownian bridge for any x satisfying x∞ → 0 as n → 8, where β = 1 for the real case and β = 2 for the complex case. Such a result indicates that the orthogonal (resp. unitary) matrices with columns being the eigenvectors of Wigner matrices are asymptotically Haar distributed on the orthogonal (resp. unitary) group from a certain perspective. © 2014 AIP Publishing LLC. | - |
| dc.language | eng | - |
| dc.relation.ispartof | Journal of Mathematical Physics | - |
| dc.title | Universality for a global property of the eigenvectors of Wigner matrices | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1063/1.4864735 | - |
| dc.identifier.scopus | eid_2-s2.0-84902283089 | - |
| dc.identifier.volume | 55 | - |
| dc.identifier.issue | 2 | - |
| dc.identifier.spage | article no. 023303 | - |
| dc.identifier.epage | article no. 023303 | - |