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Random matrix theory with an externa...
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Random matrix theory with an external source
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Random matrix theory with an external source/ by Edouard Brezin, Shinobu Hikami.
Author:
Brezin, Edouard.
other author:
Hikami, Shinobu.
Published:
Singapore :Springer Singapore : : 2016.,
Description:
xii, 138 p. :ill., digital ; : 24 cm.;
Contained By:
Springer eBooks
Subject:
Matrices. -
Online resource:
http://dx.doi.org/10.1007/978-981-10-3316-2
ISBN:
9789811033162
Random matrix theory with an external source
Brezin, Edouard.
Random matrix theory with an external source
[electronic resource] /by Edouard Brezin, Shinobu Hikami. - Singapore :Springer Singapore :2016. - xii, 138 p. :ill., digital ;24 cm. - SpringerBriefs in mathematical physics,v.192197-1757 ;. - SpringerBriefs in mathematical physics ;v.2..
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.
ISBN: 9789811033162
Standard No.: 10.1007/978-981-10-3316-2doiSubjects--Topical Terms:
528174
Matrices.
LC Class. No.: QA188 / .B74 2016
Dewey Class. No.: 512.9434
Random matrix theory with an external source
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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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Mathematics and Statistics (Springer-11649)
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