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Random Matrix Theory: Invariant Ensembles and Universality

Percy Deift Courant Institute of Mathematical Sciences, New York University, New York, NY
Dimitri Gioev University of Rochester, Rochester, NY and Wilshire Associates Inc., Santa Monica, CA
A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University
Available Formats:
Softcover ISBN: 978-0-8218-4737-4
Product Code: CLN/18
List Price: $38.00 MAA Member Price:$34.20
AMS Member Price: $30.40 This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available. Expected availability date: May 15, 2023 Electronic ISBN: 978-1-4704-1761-1 Product Code: CLN/18.E List Price:$35.00
MAA Member Price: $31.50 AMS Member Price:$28.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $57.00 MAA Member Price:$51.30
AMS Member Price: $45.60 This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available. Expected availability date: May 15, 2023 Click above image for expanded view Random Matrix Theory: Invariant Ensembles and Universality Percy Deift Courant Institute of Mathematical Sciences, New York University, New York, NY Dimitri Gioev University of Rochester, Rochester, NY and Wilshire Associates Inc., Santa Monica, CA A co-publication of the AMS and Courant Institute of Mathematical Sciences at New York University Available Formats:  Softcover ISBN: 978-0-8218-4737-4 Product Code: CLN/18  List Price:$38.00 MAA Member Price: $34.20 AMS Member Price:$30.40
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: May 15, 2023
 Electronic ISBN: 978-1-4704-1761-1 Product Code: CLN/18.E
 List Price: $35.00 MAA Member Price:$31.50 AMS Member Price: $28.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$57.00 MAA Member Price: $51.30 AMS Member Price:$45.60
This item is temporarily out of stock. Order now and your item will ship as soon as stock becomes available.
Expected availability date: May 15, 2023
• Book Details

Courant Lecture Notes
Volume: 182009; 217 pp
MSC: Primary 15; 60; 05; 62;

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.

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

• Invariant random matrix ensembles: unified derivation of eigenvalue cluster and correlation functions
• Chapter 1. Introduction and examples
• Chapter 2. Three classes of invariant ensembles
• Chapter 3. Auxiliary facts from functional analysis, Pfaffians, and three integral identities
• Chapter 4. Eigenvalue statistics for the three types of ensembles
• Universality for orthogonal and symplectic ensembles
• Chapter 5. Widom’s formulae for the $\beta =1$ and $4$ correlation kernels
• Chapter 6. Large $N$ eigenvalue statistics for the $\beta =1,4$ ensembles with monomial potentials: universality

• Reviews

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 182009; 217 pp
MSC: Primary 15; 60; 05; 62;

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.

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

• Invariant random matrix ensembles: unified derivation of eigenvalue cluster and correlation functions
• Chapter 1. Introduction and examples
• Chapter 2. Three classes of invariant ensembles
• Chapter 3. Auxiliary facts from functional analysis, Pfaffians, and three integral identities
• Chapter 4. Eigenvalue statistics for the three types of ensembles
• Universality for orthogonal and symplectic ensembles
• Chapter 5. Widom’s formulae for the $\beta =1$ and $4$ correlation kernels
• Chapter 6. Large $N$ eigenvalue statistics for the $\beta =1,4$ ensembles with monomial potentials: universality
• 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
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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