Skip to main content

Introduction to Random Matrices

Theory and Practice

  • Book
  • © 2018


Part of the book series: SpringerBriefs in Mathematical Physics (BRIEFSMAPHY, volume 26)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

eBook USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

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 analyticalresults.

Similar content being viewed by others


Table of contents (17 chapters)


“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 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

  • Department of Computer Science, University College London, London, United Kingdom

    Giacomo Livan

  • Instituto de Física, Universidade Federal de Uberlândia, Uberlândia, Brazil

    Marcel Novaes

  • Department of Mathematics, King’s College London, London, United Kingdom

    Pierpaolo Vivo

Bibliographic Information

Publish with us