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

Libro 18 de 40: SpringerBriefs in Mathematical Physics

Brézin, Edouard; Hikami, Shinobu

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

Sinopsis

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2017
Idioma
Inglés
ISBN 10 
9811033153
ISBN 13 
9789811033155
Encuadernación
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Número de edición
1
Número de páginas
152
Contacto del fabricante
no disponible
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Otras ediciones populares con el mismo título

9789811033179: Random Matrix Theory with an External Source

Edición Destacada

ISBN 10:  981103317X ISBN 13:  9789811033179
Editorial: Springer, 2017
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