Table of contents
About this book
Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.
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 analytical results.
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
- DOI https://doi.org/10.1007/978-3-319-70885-0
- Copyright Information The Author(s) 2018
- Publisher Name Springer, Cham
- eBook Packages Physics and Astronomy
- Print ISBN 978-3-319-70883-6
- Online ISBN 978-3-319-70885-0
- Series Print ISSN 2197-1757
- Series Online ISSN 2197-1765
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- Energy, Utilities & Environment