Introduction to Random Matrices: Theory and Practice

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. 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.

This is a book for absolute beginners. 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.