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The Random Matrix Theory of the Classical Compact Groups

The Random Matrix Theory of the Classical Compact Groups

$125.00 (C)

Part of Cambridge Tracts in Mathematics

  • Publication planned for: September 2019
  • availability: Not yet published - available from September 2019
  • format: Hardback
  • isbn: 9781108419529

$ 125.00 (C)
Hardback

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  • This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.

    • Presents the first book-length, in-depth treatment of these specific random matrix models made available to a broader audience
    • Assumes working knowledge of measure-theoretic probability; however more advanced probability topics, such as large deviations and measure concentration, as well as topics from other fields, such as representation theory and Riemannian manifolds, are introduced with the assumption of little previous knowledge
    • Presents a more complete picture of the field to researchers who are largely familiar with only specific corners of it
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    Reviews & endorsements

    ‘This beautiful book describes an important area of mathematics, concerning random matrices associated with the classical compact groups, in a highly accessible and engaging way. It connects a broad range of ideas and techniques, from analysis, probability theory, and representation theory to recent applications in number theory. It is a really excellent introduction to the subject.' J. P. Keating, University of Bristol

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    Product details

    • Publication planned for: September 2019
    • format: Hardback
    • isbn: 9781108419529
    • dimensions: 228 x 152 mm
    • contains: 11 b/w illus.
    • availability: Not yet published - available from September 2019
  • Table of Contents

    1. Haar measure on the classical compact matrix groups
    2. Distribution of the entries
    3. Eigenvalue distributions: exact formulas
    4. Eigenvalue distributions: asymptotics
    5. Concentration of measure
    6. Geometric applications of measure concentration
    7. Characteristic polynomials and the zeta function.

  • Author

    Elizabeth S. Meckes, Case Western Reserve University, Ohio
    Elizabeth S. Meckes is Professor of Mathematics at Case Western Reserve University, Ohio. She is a mathematical probabilist specializing in random matrix theory and its applications to other areas of mathematics, physics and statistics. She received her Ph.D. at Stanford University in 2006 and received the American Institute of Mathematics five-year fellowship. She has also received funding from the Clay Institute of Mathematics, the Simons Foundation, and the US National Science Foundation. She is the author of twenty-two research papers in mathematics, as well as the textbook Linear Algebra (Cambridge, 2018), co-authored with Mark Meckes.

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