1.

Record Nr.

UNINA9910163096303321

Autore

Brézin E.

Titolo

Random matrix theory with an external source / / by Edouard Brézin, Shinobu Hikami

Pubbl/distr/stampa

Singapore : , : Springer Singapore : , : Imprint : Springer, , 2016

ISBN

981-10-3316-1

Edizione

[1st ed. 2016.]

Descrizione fisica

1 online resource (143 pages)

Collana

SpringerBriefs in Mathematical Physics, , 2197-1757 ; ; 19

Disciplina

512.9434

Soggetti

Mathematical physics

Statistical physics

Topological groups

Lie groups

Nuclear physics

Dynamics

Mathematical Physics

Statistical Physics and Dynamical Systems

Topological Groups, Lie Groups

Particle and Nuclear Physics

Complex Systems

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di bibliografia

Includes bibliographical references and index.

Sommario/riassunto

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.