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Random matrix theory with an externa...

Brezin, Edouard.

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Random matrix theory with an external source

Record Type:	Electronic resources : 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.19..

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:

516894
Matrices.

LC Class. No.: QA188 / .B74 2016

Dewey Class. No.: 512.9434

Random matrix theory with an external source
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020 $a 9789811033162 $q (electronic bk.)
020 $a 9789811033155 $q (paper)
024 7 $a 10.1007/978-981-10-3316-2 $2 doi
035 $a 978-981-10-3316-2
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100 1 $a Brezin, Edouard. $3 3210108
245 1 0 $a Random matrix theory with an external source $h [electronic resource] / $c by Edouard Brezin, Shinobu Hikami.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2016.
300 $a xii, 138 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematical physics, $x 2197-1757 ; $v v.19
520 $a 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.
650 0 $a Matrices. $3 516894
650 0 $a Random matrices. $3 646309
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Mathematical Physics. $3 1542352
650 2 4 $a Statistical Physics and Dynamical Systems. $3 3135115
650 2 4 $a Topological Groups, Lie Groups. $3 891005
650 2 4 $a Particle and Nuclear Physics. $3 1067136
650 2 4 $a Complex Systems. $3 1566441
700 1 $a Hikami, Shinobu. $3 3210109
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematical physics ; $v v.19. $3 3210110
856 4 0 $u http://dx.doi.org/10.1007/978-981-10-3316-2
950 $a Mathematics and Statistics (Springer-11649)