An Introduction to Random Matrices (Cambridge Studies in Advanced Mathematics)

Anderson, Greg W./ Guionnet, Alice/ Zeitouni, Ofer

Cambridge University Press（2009/11発売）

• 製本 Hardcover:ハードカバー版／ページ数 508 p.／サイズ 75 exercises
• 言語 ENG
• 商品コード 9780521194525
• DDC分類 512.9434

基本説明

A graduate level textbook.

Full Description

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.

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.