---

＜電子ブック＞
Random Matrix Theory with an External Source / by Edouard Brézin, Shinobu Hikami
(SpringerBriefs in Mathematical Physics. ISSN:21971765 ; 19)

版	1st ed. 2016.
出版者	(Singapore : Springer Nature Singapore : Imprint: Springer)
出版年	2016
大きさ	XII, 138 p : online resource
著者標目	*Brézin, Edouard author Hikami, Shinobu author SpringerLink (Online service)
件　名	LCSH:Mathematical physics LCSH:Topological groups LCSH:Lie groups LCSH:Nuclear physics LCSH:System theory FREE:Mathematical Physics FREE:Theoretical, Mathematical and Computational Physics FREE:Topological Groups and Lie Groups FREE:Nuclear and Particle Physics FREE:Complex Systems
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-981-10-3316-2

 類似資料