Introduction to Random Matrices Theory and Practice [Paperback]

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, Wigners 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.

The text is well written, and the authors informal conversational style sets the book up nicely for someone who is using it as a self-study guide in the area. The chapters are short, but there are numerous examples, and the most instructive calculations are represented in full. Particular attention is paid to the numerical verification of the most analytical results. (Susanna Spektor, Mathematical Reviews, September, 2018)

Giacomo Livan, Marcel Novaes, and Pierpaolo Vivo have written a smallc&