Random Matrix Theory with an External Source

Nonfiction, Science & Nature, Mathematics, Group Theory, Science, Physics, Mathematical Physics
Cover of the book Random Matrix Theory with an External Source by Edouard Brézin, Shinobu Hikami, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Edouard Brézin, Shinobu Hikami ISBN: 9789811033162
Publisher: Springer Singapore Publication: January 11, 2017
Imprint: Springer Language: English
Author: Edouard Brézin, Shinobu Hikami
ISBN: 9789811033162
Publisher: Springer Singapore
Publication: January 11, 2017
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Singapore

Cover of the book Restructuring Translation Education by Edouard Brézin, Shinobu Hikami
Cover of the book IT Convergence and Security 2017 by Edouard Brézin, Shinobu Hikami
Cover of the book Language Curriculum Innovation in a Chinese Secondary School by Edouard Brézin, Shinobu Hikami
Cover of the book Observed Climate Variability and Change over the Indian Region by Edouard Brézin, Shinobu Hikami
Cover of the book Security in Computing and Communications by Edouard Brézin, Shinobu Hikami
Cover of the book CO2, Temperature, and Trees by Edouard Brézin, Shinobu Hikami
Cover of the book Therapy of Social Medicine by Edouard Brézin, Shinobu Hikami
Cover of the book Theory and Methods of Quantification Design on System-Level Electromagnetic Compatibility by Edouard Brézin, Shinobu Hikami
Cover of the book Japanese Imperialism: Politics and Sport in East Asia by Edouard Brézin, Shinobu Hikami
Cover of the book Proceedings of Sixth International Conference on Soft Computing for Problem Solving by Edouard Brézin, Shinobu Hikami
Cover of the book Principles of Imprecise-Information Processing by Edouard Brézin, Shinobu Hikami
Cover of the book Dynamics and Vibration Analyses of Gearbox in Wind Turbine by Edouard Brézin, Shinobu Hikami
Cover of the book Recent Trends in Signal and Image Processing by Edouard Brézin, Shinobu Hikami
Cover of the book China Satellite Navigation Conference (CSNC) 2016 Proceedings: Volume III by Edouard Brézin, Shinobu Hikami
Cover of the book Fast Reactor System Design by Edouard Brézin, Shinobu Hikami
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy