**Courant Lecture Notes**

Volume: 18;
2009;
217 pp;
Softcover

MSC: Primary 15; 60; 05; 62;

Print ISBN: 978-0-8218-4737-4

Product Code: CLN/18

List Price: $35.00

Individual Member Price: $28.00

**Electronic ISBN: 978-1-4704-1761-1
Product Code: CLN/18.E**

List Price: $35.00

Individual Member Price: $28.00

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#### Supplemental Materials

# Random Matrix Theory: Invariant Ensembles and Universality

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*Percy Deift; Dimitri Gioev*

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University

This book features a unified derivation of the mathematical theory of
the three classical types of invariant random matrix
ensembles—orthogonal, unitary, and symplectic. The authors
follow the approach of Tracy and Widom, but the exposition here
contains a substantial amount of additional material, in particular,
facts from functional analysis and the theory of Pfaffians. The main
result in the book is a proof of universality for orthogonal and
symplectic ensembles corresponding to generalized Gaussian type
weights following the authors' prior work. New, quantitative error
estimates are derived.

The book is based in part on a graduate course given by the first
author at the Courant Institute in fall 2005. Subsequently, the second
author gave a modified version of this course at the University of
Rochester in spring 2007. Anyone with some background in complex
analysis, probability theory, and linear algebra and an interest in
the mathematical foundations of random matrix theory will benefit from
studying this valuable reference.

Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

#### Readership

Graduate students and research mathematicians interested in mathematical foundations of random matrix theory.

#### Reviews & Endorsements

Anyone with some background in complex analysis, probability theory, and linear algebra and an interest in the mathematical foundations of random matrix theory will benefit from studying this valuable reference.

-- Zentralblatt MATH

#### Table of Contents

# Table of Contents

## Random Matrix Theory: Invariant Ensembles and Universality

- Cover Cover11
- General editor information ii3
- Title page iii4
- Contents vii8
- Preface ix10
- Part 1: Invariant random matrix ensembles: unified derivation of eigenvalue cluster and correlation functions 112
- Introduction and examples 314
- Three classes of invariant ensembles 920
- Auxiliary facts from functional analysis, Pfaffians, and three integral identities 3748
- Eigenvalue statistics for the three types of ensembles 6576
- Part 2: Universality for orthogonal and symplectic ensembles 113124
- Widom’s formulae for the 𝛽=1 and 4 correlation kernels 115126
- Large 𝑁 eigenvalue statistics for the 𝛽=1,4 ensembles with monomial potentials: universality 139150
- Bibliography 211222
- Index 217228
- Back Cover Back Cover1231