Topics in Random Matrix Theory

by Terence Tao

The field of random matrix theory has seen an explosion of activity in recent years, with connections to many areas of mathematics and physics. However, this makes the current state of the field almost too large to survey in a single book. In this graduate text, we focus on one specific sector of the field, namely the spectral distribution of random Wigner matrix ensembles (such as the Gaussian Unitary Ensemble), as well as iid matrix ensembles. The text is largely self-contained and starts with a review of relevant aspects of probability theory and linear algebra. With over 200 exercises, the book is suitable as an introductory text for beginning graduate students seeking to enter the field.

Genres: Mathematics, Physics, Textbooks

282 pages, Hardcover

First published April 1, 2012

About the author

Terence "Terry" Tao FAA FRS (simplified Chinese: 陶哲轩; traditional Chinese: 陶哲軒; pinyin: Táo Zhéxuān) is an Australian-American mathematician who has worked in various areas of mathematics. He currently focuses on harmonic analysis, partial differential equations, algebraic combinatorics, arithmetic combinatorics, geometric combinatorics, compressed sensing and analytic number theory. As of 2015, he holds the James and Carol Collins chair in mathematics at the University of California, Los Angeles. Tao was a co-recipient of the 2006 Fields Medal and the 2014 Breakthrough Prize in Mathematics.

Reviews

[Jingyuan · Rating 5 out of 5]

Good intro to RMT.

[Kevin K. Gillette · Rating 4 out of 5]

Prof. Tao has produced a wonderful graduate text that, despite the specificity of the title, is really a journey through a lot of mathematical statistics, calculus, modern algebra, topology, and functional analysis. I highly recommend this book for a graduate course in stochastic processes. Prof. Tao not only leads the reader through numerous classical results (I count at least five different proofs of the Central Limit Theorem, for example), but provides a window into the thought process of a professional mathematician working in somewhat uncharted waters vis-a-vis proofs via heuristic arguments, to be supplemented as needed with rigor.

A worthwhile read, all in all!