Random Matrix Theory with an External Source

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

Expresses the correlation function of the Gaussian random matrix model with an external source in the integral formula

Examines universal behaviors of level spacing distributions for an arbitrary external source

Obtains the topological invariants such as the intersection numbers of the moduli space of spin curves by the duality and replica method in the scaling limit of the external source

Includes supplementary material: [...]

Details

Erscheinungsjahr:	2017
Fachbereich:	Allgemeines
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xii 138 S.
ISBN-13:	9789811033155
ISBN-10:	9811033153
Sprache:	Englisch
Herstellernummer:	978-981-10-3315-5
Einband:	Kartoniert / Broschiert
Autor:	Hikami, Shinobu Brézin, Edouard
Auflage:	1st edition 2016
Hersteller:	Springer Singapore Springer Nature Singapore
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	Shinobu Hikami (u. a.)
Erscheinungsdatum:	17.01.2017
Gewicht:	0,242 kg