Progress on the Study of the Ginibre Ensembles
This open access book focuses on the Ginibre ensembles that are non-Hermitian random matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within random matrix theory, featuring, for example, the first book on the subject written by Mehta in 1967. Their status has been...
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| Sprache: | Englisch |
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Springer Nature
2024
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| Online-Zugang: | ONIX_20240913_9789819751730_43 |
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| author | Byun, Sung-Soo Forrester, Peter J. |
| author_browse | Byun, Sung-Soo Forrester, Peter J. |
| author_facet | Byun, Sung-Soo Forrester, Peter J. |
| author_sort | Byun, Sung-Soo |
| collection | Directory of Open Access Books |
| description | This open access book focuses on the Ginibre ensembles that are non-Hermitian random matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within random matrix theory, featuring, for example, the first book on the subject written by Mehta in 1967. Their status has been consolidated and extended over the following years, as more applications have come to light, and the theory has developed to greater depths. This book sets about detailing much of this progress. Themes covered include eigenvalue PDFs and correlation functions, fluctuation formulas, sum rules and asymptotic behaviors, normal matrix models, and applications to quantum many-body problems and quantum chaos. There is a distinction between the Ginibre ensemble with complex entries (GinUE) and those with real or quaternion entries (GinOE and GinSE, respectively). First, the eigenvalues of GinUE form a determinantal point process, while those of GinOE and GinSE have the more complicated structure of a Pfaffian point process. Eigenvalues on the real line in the case of GinOE also provide another distinction. On the other hand, the increased complexity provides new opportunities for research. This is demonstrated in our presentation, which details several applications and contains not previously published theoretical advances. The areas of application are diverse, with examples being diffusion processes and persistence in statistical physics and equilibria counting for a system of random nonlinear differential equations in the study of the stability of complex systems. |
| format | Online |
| id | doab-20.500.12854ir-144761 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2024 |
| publishDateRange | 2024 |
| publishDateSort | 2024 |
| publisher | Springer Nature |
| publisherStr | Springer Nature |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1447612024-09-14T04:31:39Z Progress on the Study of the Ginibre Ensembles Byun, Sung-Soo Forrester, Peter J. Ginibre Ensembles Non-Hermitian Random Matrices Determinantal Point Processes Pfaffan Point Processes Orthogonal Polynomials in the Complex Plane Skew Orthogonal Polynomials Two-Dimensional Coulomb Gas Normal Matrix Model Fluctuation Formulas thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWL Stochastics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations This open access book focuses on the Ginibre ensembles that are non-Hermitian random matrices proposed by Ginibre in 1965. Since that time, they have enjoyed prominence within random matrix theory, featuring, for example, the first book on the subject written by Mehta in 1967. Their status has been consolidated and extended over the following years, as more applications have come to light, and the theory has developed to greater depths. This book sets about detailing much of this progress. Themes covered include eigenvalue PDFs and correlation functions, fluctuation formulas, sum rules and asymptotic behaviors, normal matrix models, and applications to quantum many-body problems and quantum chaos. There is a distinction between the Ginibre ensemble with complex entries (GinUE) and those with real or quaternion entries (GinOE and GinSE, respectively). First, the eigenvalues of GinUE form a determinantal point process, while those of GinOE and GinSE have the more complicated structure of a Pfaffian point process. Eigenvalues on the real line in the case of GinOE also provide another distinction. On the other hand, the increased complexity provides new opportunities for research. This is demonstrated in our presentation, which details several applications and contains not previously published theoretical advances. The areas of application are diverse, with examples being diffusion processes and persistence in statistical physics and equilibria counting for a system of random nonlinear differential equations in the study of the stability of complex systems. 2024-09-14T04:31:36Z 2024-09-14T04:31:36Z 2024-09-13T12:59:49Z 2025 book ONIX_20240913_9789819751730_43 https://library.oapen.org/handle/20.500.12657/93276 9789819751730 9789819751723 https://directory.doabooks.org/handle/20.500.12854/144761 eng KIAS Springer Series in Mathematics open access image/jpeg n/a https://library.oapen.org/bitstream/20.500.12657/93276/1/978-981-97-5173-0.pdf Springer Nature Springer Nature Singapore 10.1007/978-981-97-5173-0 10.1007/978-981-97-5173-0 9fa3421d-f917-4153-b9ab-fc337c396b5a 8d21921b-08e1-49d0-9d8f-781f43c29843 f16c1d88-2f23-41b2-8bed-c5bd86579d2e 5e452ab8-4208-4b50-b696-5925a0b8712b d9d1986f-9387-459b-8f7a-11b7716b97f2 9789819751730 9789819751723 Springer Nature Singapore 221 Singapore [...] [...] Seoul National University 서울대학교 10.13039/501100002551 POSCO TJ Park Foundation 포스코청암재단 10.13039/100015506 open access |
| spellingShingle | Ginibre Ensembles Non-Hermitian Random Matrices Determinantal Point Processes Pfaffan Point Processes Orthogonal Polynomials in the Complex Plane Skew Orthogonal Polynomials Two-Dimensional Coulomb Gas Normal Matrix Model Fluctuation Formulas thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWL Stochastics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations Byun, Sung-Soo Forrester, Peter J. Progress on the Study of the Ginibre Ensembles |
| title | Progress on the Study of the Ginibre Ensembles |
| title_full | Progress on the Study of the Ginibre Ensembles |
| title_fullStr | Progress on the Study of the Ginibre Ensembles |
| title_full_unstemmed | Progress on the Study of the Ginibre Ensembles |
| title_short | Progress on the Study of the Ginibre Ensembles |
| title_sort | progress on the study of the ginibre ensembles |
| topic | Ginibre Ensembles Non-Hermitian Random Matrices Determinantal Point Processes Pfaffan Point Processes Orthogonal Polynomials in the Complex Plane Skew Orthogonal Polynomials Two-Dimensional Coulomb Gas Normal Matrix Model Fluctuation Formulas thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWL Stochastics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations |
| topic_facet | Ginibre Ensembles Non-Hermitian Random Matrices Determinantal Point Processes Pfaffan Point Processes Orthogonal Polynomials in the Complex Plane Skew Orthogonal Polynomials Two-Dimensional Coulomb Gas Normal Matrix Model Fluctuation Formulas thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics::PBWL Stochastics thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations |
| url | ONIX_20240913_9789819751730_43 |
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