Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach
Abstract Using large N arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large N limit. The setting generalizes the quaternionic extension of free probability to two-point functions. In the particular case of biunitari...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1007/JHEP06(2018)152 |
| _version_ | 1818324809269903360 |
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| author | Maciej A. Nowak Wojciech Tarnowski |
| author_facet | Maciej A. Nowak Wojciech Tarnowski |
| author_sort | Maciej A. Nowak |
| collection | DOAJ |
| description | Abstract Using large N arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large N limit. The setting generalizes the quaternionic extension of free probability to two-point functions. In the particular case of biunitarily invariant random matrices, we obtain a simple, general expression for the two-point eigenvector correlation function, which can be viewed as a further generalization of the single ring theorem. This construction has some striking similarities to the freeness of the second kind known for the Hermitian ensembles in large N. On the basis of several solved examples, we conjecture two kinds of microscopic universality of the eigenvectors — one in the bulk, and one at the rim. The form of the conjectured bulk universality agrees with the scaling limit found by Chalker and Mehlig [JT Chalker, B Mehlig, Phys. Rev. Lett. 81 (1998) 3367] in the case of the complex Ginibre ensemble. |
| first_indexed | 2024-12-13T11:34:29Z |
| format | Article |
| id | doaj.art-5738ffb375c94f3fb3f2e354d0589f99 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-13T11:34:29Z |
| publishDate | 2018-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-5738ffb375c94f3fb3f2e354d0589f992022-12-21T23:47:50ZengSpringerOpenJournal of High Energy Physics1029-84792018-06-012018613410.1007/JHEP06(2018)152Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approachMaciej A. Nowak0Wojciech Tarnowski1M. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian UniversityM. Smoluchowski Institute of Physics and Mark Kac Complex Systems Research Center, Jagiellonian UniversityAbstract Using large N arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large N limit. The setting generalizes the quaternionic extension of free probability to two-point functions. In the particular case of biunitarily invariant random matrices, we obtain a simple, general expression for the two-point eigenvector correlation function, which can be viewed as a further generalization of the single ring theorem. This construction has some striking similarities to the freeness of the second kind known for the Hermitian ensembles in large N. On the basis of several solved examples, we conjecture two kinds of microscopic universality of the eigenvectors — one in the bulk, and one at the rim. The form of the conjectured bulk universality agrees with the scaling limit found by Chalker and Mehlig [JT Chalker, B Mehlig, Phys. Rev. Lett. 81 (1998) 3367] in the case of the complex Ginibre ensemble.http://link.springer.com/article/10.1007/JHEP06(2018)152Matrix ModelsRandom Systems |
| spellingShingle | Maciej A. Nowak Wojciech Tarnowski Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach Journal of High Energy Physics Matrix Models Random Systems |
| title | Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach |
| title_full | Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach |
| title_fullStr | Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach |
| title_full_unstemmed | Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach |
| title_short | Probing non-orthogonality of eigenvectors in non-Hermitian matrix models: diagrammatic approach |
| title_sort | probing non orthogonality of eigenvectors in non hermitian matrix models diagrammatic approach |
| topic | Matrix Models Random Systems |
| url | http://link.springer.com/article/10.1007/JHEP06(2018)152 |
| work_keys_str_mv | AT maciejanowak probingnonorthogonalityofeigenvectorsinnonhermitianmatrixmodelsdiagrammaticapproach AT wojciechtarnowski probingnonorthogonalityofeigenvectorsinnonhermitianmatrixmodelsdiagrammaticapproach |