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Field name	Details
Dewey Class	530.15
Title	Random Matrix Theory with an External Source ([EBook]) / by Edouard Brézin, Shinobu Hikami.
Author	Brézin, Edouard
Added Personal Name	Hikami, Shinobu author.
Other name(s)	SpringerLink (Online service)
Publication	Singapore : : Springer Singapore : : Imprint: Springer, , 2016.
Physical Details	XII, 138 p. : online resource.
Series	SpringerBriefs in Mathematical Physics 2197-1757 ; ; 19
ISBN	9789811033162
Summary Note	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.:
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-981-10-3316-2
Links to Related Works	Subject References: Complex Systems . Lie groups . Mathematical Physics . Mathematics . Nuclear Physics . Particle and Nuclear Physics . Statistical Physics and Dynamical Systems . System theory . Topological groups . Topological groups, Lie groups . Authors: Brézin, Edouard . Hikami, Shinobu . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematical Physics . Classification: 530.15 .

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Random Matrix Theory with an External Source

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