An Introduction to Random Matrices

by Greg W. Anderson, Alice Guionnet, Ofer Zeitouni

Overview

The theory of random matrices plays an important role in many areas of pure mathematics and employs a variety of sophisticated mathematical tools (analytical, probabilistic and combinatorial). This diverse array of tools, while attesting to the vitality of the field, presents several formidable obstacles to the newcomer, and even the expert probabilist. This rigorous introduction to the basic theory is sufficiently self-contained to be accessible to graduate students in mathematics or related sciences, who have mastered probability theory at the graduate level, but have not necessarily been exposed to advanced notions of functional analysis, algebra or geometry. Useful background material is collected in the appendices and exercises are also included throughout to test the reader's understanding. Enumerative techniques, stochastic analysis, large deviations, concentration inequalities, disintegration and Lie algebras all are introduced in the text, which will enable readers to approach the research literature with confidence.

Product Details

ISBN-13:	9780521194525
Publisher:	Cambridge University Press
Publication date:	11/19/2009
Series:	Cambridge Studies in Advanced Mathematics , #118
Edition description:	New Edition
Pages:	508
Product dimensions:	6.20(w) x 9.00(h) x 1.20(d)

About the Author

Greg W. Anderson is Professor in the School of Mathematics at the University of Minnesota.

Alice Guionnet is Director of Research at the Ecole Normale Supérieure in Lyon and the Centre National de la Recherche Scientifique (CNRS).

Ofer Zeitouni is Professor of Mathematics at both the University of Minnesota and the Weizmann Institute of Science, Israel.

Table of Contents

Preface; 1. Introduction; 2. Real and complex Wigner matrices; 3. Hermite polynomials, spacings, and limit distributions for the Gaussian ensembles; 4. Some generalities; 5. Free probability; Appendices; Bibliography; General conventions; Glossary; Index.

Editorial Reviews

"... the authors here have done an admirable job in presenting in a coherent and self-contained fashion a significant number of "core" topics of random matrix theory... this is a very valuable new reference for the subject, incorporating many modern results and perspectives that are not present in earlier texts on this topic. This book would serve as an excellent foundation with which to begin studying other aspects of random matrix theory."
Terence Tao, Mathematical Reviews

From the Publisher