An Introduction to Random Matrices

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

Greg W. Anderson (Author), Alice Guionnet (Author), Ofer Zeitouni (Author)

9780521194525, Cambridge University Press

Hardback, published 19 November 2009

508 pages, 7 b/w illus. 75 exercises
22.9 x 15.5 x 2.8 cm, 0.84 kg

'… the book aims to introduce some of the modern techniques of random matrix theory in a comprehensive and rigorous way. It has a broad range of topics and most of them are fairly accessible. The focus is on introducing and explaining the main techniques, rather than obtaining the most general results. Additional references are given for the reader who wants to continue the study of a certain topic. The writing style is careful and the book is mostly self-contained with complete proofs. This is an excellent new contribution to random matrix theory.' Journal of Approximation Theory

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.

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.

Subject Areas: Probability & statistics [PBT], Calculus & mathematical analysis [PBK], Algebra [PBF]