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An Introduction to Random Matrices


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: November 2009
  • availability: Available
  • format: Hardback
  • isbn: 9780521194525

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About the Authors
  • 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.

    • A rigorous yet accessible introduction for beginners at the graduate level
    • Contains over 70 exercises so the reader can test their understanding of the material
    • A valuable text not only for mathematicians, but also physicists and electrical engineers
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    Reviews & endorsements

    ' … this is a very valuable new reference for the subject, incorporating many modern results and perspectives that are not present in earlier texts on this topic … this book would serve as an excellent foundation with which to begin studying other aspects of random matrix theory.' Terence Tao, Mathematical Reviews

    '… 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

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    Product details

    • Date Published: November 2009
    • format: Hardback
    • isbn: 9780521194525
    • length: 508 pages
    • dimensions: 229 x 155 x 28 mm
    • weight: 0.84kg
    • contains: 7 b/w illus. 75 exercises
    • availability: Available
  • Table of Contents

    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
    General conventions

  • Resources for

    An Introduction to Random Matrices

    Greg W. Anderson, Alice Guionnet, Ofer Zeitouni

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  • Authors

    Greg W. Anderson, University of Minnesota
    Greg W. Anderson is Professor in the School of Mathematics at the University of Minnesota.

    Alice Guionnet, Ecole Normale Supérieure, Lyon
    Alice Guionnet is Director of Research at the Ecole Normale Supérieure in Lyon and the Centre National de la Recherche Scientifique (CNRS).

    Ofer Zeitouni, Weizmann Institute/University of Minnesota
    Ofer Zeitouni is Professor of Mathematics at both the University of Minnesota and the Weizmann Institute of Science, Israel.

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