Skip to content
Register Sign in Wishlist

Random Matrices: High Dimensional Phenomena

$61.99 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: November 2009
  • availability: Available
  • format: Paperback
  • isbn: 9780521133128

$ 61.99 (C)

Add to cart Add to wishlist

Other available formats:

Looking for an examination copy?

This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact providing details of the course you are teaching.

Product filter button
About the Authors
  • This book focuses on the behavior of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.

    • A modern theoretical treatment that includes new results and proofs
    • Contains introductory material and summaries of key points to make the book easily accessible to non-specialists
    • Its rigorous presentation means the book is still suitably comprehensive for mathematicians
    Read more

    Reviews & endorsements

    "The book under review is somewhat special in that it is not so much an introduction to the standard models and topics of random matrix theory, but rather to a set of functional analytic issues that are relevant to random matrices."
    Michael Stolz, Mathematical Reviews

    Customer reviews

    Not yet reviewed

    Be the first to review

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Date Published: November 2009
    • format: Paperback
    • isbn: 9780521133128
    • length: 448 pages
    • dimensions: 228 x 150 x 22 mm
    • weight: 0.63kg
    • contains: 75 exercises
    • availability: Available
  • Table of Contents

    1. Metric Measure spaces
    2. Lie groups and matrix ensembles
    3. Entropy and concentration of measure
    4. Free entropy and equilibrium
    5. Convergence to equilibrium
    6. Gradient ows and functional inequalities
    7. Young tableaux
    8. Random point fields and random matrices
    9. Integrable operators and differential equations
    10. Fluctuations and the Tracy–Widom distribution
    11. Limit groups and Gaussian measures
    12. Hermite polynomials
    13. From the Ornstein–Uhlenbeck process to Burger's equation
    14. Noncommutative probability spaces

  • Author

    Gordon Blower, Lancaster University
    Gordon Blower is currently Head of the Department of Mathematics and Statistics at Lancaster University, and Professor of Mathematical Analysis.

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.