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Random Matrix Theory: Invariant Ensembles and Universality
Percy Deift, Courant Institute of Mathematical Sciences, New York University, NY, and Dimitri Gioev, University of 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.
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Courant Lecture Notes
2009; 217 pp; softcover
Volume: 18
ISBN-10: 0-8218-4737-6
ISBN-13: 978-0-8218-4737-4
List Price: US$33
Member Price: US$26.40
Order Code: CLN/18
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See also:

Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach - Percy Deift

Integrable Systems and Random Matrices: In Honor of Percy Deift - Jinho Baik, Thomas Kriecherbauer, Luen-Chau Li, Kenneth D T-R McLaughlin and Carlos Tomei

Random Matrices, Frobenius Eigenvalues, and Monodromy - Nicholas M Katz and Peter Sarnak

Skew-Orthogonal Polynomials and Random Matrix Theory - Saugata Ghosh

Eigenvalue Distribution of Large Random Matrices - Leonid Pastur and Mariya Shcherbina

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

"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

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