Random Matrix Theory with an External Source: 19 (SpringerBriefs in Mathematical Physics) - Softcover

Buch 18 von 40: SpringerBriefs in Mathematical Physics

Brézin, Edouard; Hikami, Shinobu

 
9789811033155: Random Matrix Theory with an External Source: 19 (SpringerBriefs in Mathematical Physics)
Softcover
ISBN 10: 9811033153 ISBN 13: 9789811033155
Verlag: Springer, 2017

Inhaltsangabe

This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.

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Reseña del editor

This is a first book to show that the theory of the Gaussian random matrix is essential to understand the universal correlations with random fluctuations and to demonstrate that it is useful to evaluate topological universal quantities. We consider Gaussian random matrix models in the presence of a deterministic matrix source. In such models the correlation functions are known exactly for an arbitrary source and for any size of the matrices. The freedom given by the external source allows for various tunings to different classes of universality. The main interest is to use this freedom to compute various topological invariants for surfaces such as the intersection numbers for curves drawn on a surface of given genus with marked points, Euler characteristics, and the Gromov–Witten invariants. A remarkable duality for the average of characteristic polynomials is essential for obtaining such topological invariants. The analysis is extended to nonorientable surfaces and to surfaces with boundaries.

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Verlag
Springer
Erscheinungsdatum
2017
Sprache
Englisch
ISBN 10 
9811033153
ISBN 13 
9789811033155
Einband
Tapa blanda
Auflage
1
Anzahl der Seiten
152
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Verlag: Springer, 2017
Softcover