國立虎尾科技大學 |

Progress on the study of the Ginibre ensembles

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Progress on the study of the Ginibre ensembles/ by Sung-Soo Byun, Peter J. Forrester.
作者:	Byun, Sung-Soo.
其他作者:	Forrester, Peter J.
出版者:	Singapore :Springer Nature Singapore : : 2025.,
面頁冊數:	xi, 221 p. :ill., digital ; : 24 cm.;
Contained By:	Springer Nature eBook
標題:	Differential Equations. -
電子資源:	https://doi.org/10.1007/978-981-97-5173-0
ISBN:	9789819751730

Progress on the study of the Ginibre ensembles
Byun, Sung-Soo.

Progress on the study of the Ginibre ensembles[electronic resource] /by Sung-Soo Byun, Peter J. Forrester. - Singapore :Springer Nature Singapore :2025. - xi, 221 p. :ill., digital ;24 cm. - KIAS Springer series in mathematics,v. 32731-5150 ;. - KIAS Springer series in mathematics ;v. 3..

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.

Open access.

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.

ISBN: 9789819751730

Standard No.: 10.1007/978-981-97-5173-0doiSubjects--Topical Terms:

681826
Differential Equations.

LC Class. No.: QA196.5

Dewey Class. No.: 512.9434

Progress on the study of the Ginibre ensembles
LDR:03140nam a2200373 a 4500 001 1160494
003 DE-He213
005 20240821130231.0
006 m d
007 cr nn 008maaau
008 251029s2025 si s 0 eng d
020 $a 9789819751730 $q (electronic bk.)
020 $a 9789819751723 $q (paper)
024 7 $a 10.1007/978-981-97-5173-0 $2 doi
035 $a 978-981-97-5173-0
040 $a GP $c GP
041 0 $a eng
050 4 $a QA196.5
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 512.9434 $2 23
090 $a QA196.5 $b .B998 2025
100 1 $a Byun, Sung-Soo. $3 1487544
245 1 0 $a Progress on the study of the Ginibre ensembles $h [electronic resource] / $c by Sung-Soo Byun, Peter J. Forrester.
260 $a Singapore : $c 2025. $b Springer Nature Singapore : $b Imprint: Springer,
300 $a xi, 221 p. : $b ill., digital ; $c 24 cm.
490 1 $a KIAS Springer series in mathematics, $x 2731-5150 ; $v v. 3
505 0 $a 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.
506 $a Open access.
520 $a 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.
650 2 4 $a Differential Equations. $3 681826
650 2 4 $a Mathematical Physics. $3 786661
650 1 4 $a Probability Theory. $3 1366244
650 0 $a Probabilities. $3 527847
650 0 $a Eigenvalues. $3 527710
650 0 $a Random matrices. $3 678171
700 1 $a Forrester, Peter J. $3 1487545
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
830 0 $a KIAS Springer series in mathematics ; $v v. 3. $3 1487546
856 4 0 $u https://doi.org/10.1007/978-981-97-5173-0
950 $a Mathematics and Statistics (SpringerNature-11649)