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 email@example.com providing details of the course you are teaching.
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.Read more
- 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
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
Not yet reviewed
Be the first to review
Review was not posted due to profanity×
- 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
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email firstname.lastname@example.orgRegister Sign in
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.Continue ×
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.×