Progress on the Study of the Ginibre Ensembles
Springer Verlag, Singapore
978-981-97-5172-3 (ISBN)
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.
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.
Sung-Soo Byun is Assistant Professor in the Department of Mathematical Sciences at Seoul National University. Peter J. Forrester is Professor in School of Mathematics and Statistics at The University of Melbourne.
Introduction.- Eigenvalue PDFs and Correlations.- Fluctuation Formulas.- Coulomb Gas Model, Sum Rules and Asymptotic Behaviours.- Normal Matrix Models.- Further Theory and Applications.- Eigenvalue Statistics for GinOE and Elliptic GinOE.- Analogues of GinUE Statistical Properties for GinOE.- Further Extensions to GinOE.- Statistical Properties of GinSE and Elliptic GinSE.- Further Extensions to GinSE.
| Erscheinungsdatum | 22.08.2024 |
|---|---|
| Reihe/Serie | KIAS Springer Series in Mathematics |
| Zusatzinfo | 7 Illustrations, black and white |
| Verlagsort | Singapore |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik |
| Naturwissenschaften ► Physik / Astronomie | |
| Schlagworte | Determinantal Point Processes • Fluctuation Formulas • Ginibre Ensembles • Non-Hermitian Random Matrices • Normal Matrix Model • open access • Orthogonal Polynomials in the Complex Plane • Pfaffan Point Processes • Skew Orthogonal Polynomials • Two-Dimensional Coulomb Gas |
| ISBN-10 | 981-97-5172-1 / 9819751721 |
| ISBN-13 | 978-981-97-5172-3 / 9789819751723 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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