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- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 26)
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Table of contents (17 chapters)
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Front Matter
About this book
The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).
Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analyticalresults.
Keywords
- Coulomb Gas Approach
- Diagrammatic Method
- Edwards-Jones Replica Theory
- Gaussian Matrices
- Random Matrices with Real Spectrum
- Resolvent Method
- Tracy-Widom Law
- Wigner's Semicircle Law
- Wishart Matrices
- Wigner surmise
- Joint probability density function of eigenvalues
- Jpdf of eigenvalues
- Vandermonde matrix
- Vandermonde determinant
- Andreief indentity
- Wishart-Laguerre ensemble
- Marcenko-Pastur distribution
- Gaussian Orthogonal Ensemble
- Edwards-Jones formalism
- Dyson Coulomb gas
Reviews
“Giacomo Livan, Marcel Novaes, and Pierpaolo Vivo have written a small but lively book on random matrices. … The book feels conversational. It has an informal tone, a sense of humor, and a pleasant mixture of exposition and detail. The pace is brisk, appropriate for a book aiming to be an introductory survey rather than a formal textbook.” (John D. Cook, MAA Reviews, July, 2018)
“The emphasis is on concepts, computations and tricks of the trade, and the style is modern and informal, which the reader will no doubt enjoy. … This monograph should prove to become a very welcome companion to the serious and enthusiastic reader setting out to get to know this vast and very useful subject.” (Rabe von Randow, zbMATH 1386.15003, 2018)
Authors and Affiliations
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Department of Computer Science, University College London, London, United Kingdom
Giacomo Livan
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Instituto de Física, Universidade Federal de Uberlândia, Uberlândia, Brazil
Marcel Novaes
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Department of Mathematics, King’s College London, London, United Kingdom
Pierpaolo Vivo
Bibliographic Information
Book Title: Introduction to Random Matrices
Book Subtitle: Theory and Practice
Authors: Giacomo Livan, Marcel Novaes, Pierpaolo Vivo
Series Title: SpringerBriefs in Mathematical Physics
DOI: https://doi.org/10.1007/978-3-319-70885-0
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Author(s) 2018
Softcover ISBN: 978-3-319-70883-6Published: 25 January 2018
eBook ISBN: 978-3-319-70885-0Published: 16 January 2018
Series ISSN: 2197-1757
Series E-ISSN: 2197-1765
Edition Number: 1
Number of Pages: IX, 124
Number of Illustrations: 10 illustrations in colour
Topics: Mathematical Methods in Physics, Probability Theory and Stochastic Processes, Mathematical Physics, Statistical Physics and Dynamical Systems, Complex Systems