Progress on the Study of the Ginibre Ensembles - Couverture souple

Byun, Sung-Soo; Forrester, Peter J.

Couverture souple

ISBN 10 : 9819751756 ISBN 13 : 9789819751754

Editeur : Springer, 2025

Synopsis

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.

A propos du livre

À propos de l'auteur

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2025
• Langue: anglais
• ISBN 10: 9819751756
• ISBN 13: 9789819751754
• Reliure: Broché
• Nombre de pages: 236
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne