Introduction to Random Matrices Theory and Practice /

• Main Authors: Livan, Giacomo (Author, http://id.loc.gov/vocabulary/relators/aut), Novaes, Marcel (http://id.loc.gov/vocabulary/relators/aut), Vivo, Pierpaolo (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: SpringerBriefs in Mathematical Physics, 26
• Subjects: Physics.; Probabilities.; Mathematical physics.; Statistical physics.; Dynamical systems.; Mathematical Methods in Physics.; Probability Theory and Stochastic Processes.; Mathematical Physics.; Statistical Physics and Dynamical Systems.; Complex Systems.

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 forma...

Table of Contents:

• Preface
• Getting Started
• Value the eigenvalue
• Classified Material
• The fluid semicircle
• Saddle-point-of-view
• Time for a change
• Meet Vandermonde
• Resolve(nt) the semicircle
• One pager on eigenvectors
• Finite N
• Meet Andréief
• Finite N is not finished
• Classical Ensembles:Wishart-Laguerre
• Meet Marčenko and Pastur
• Replicas
• Replicas for GOE
• Born to be free.