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Random Matrices: High Dimensional Phenomena
Contributor(s): Blower, Gordon (Author)
ISBN: 0521133122     ISBN-13: 9780521133128
Publisher: Cambridge University Press
OUR PRICE:   $63.64  
Product Type: Paperback - Other Formats
Published: November 2009
Qty:
Annotation: An introduction to the behaviour of random matrices. Suitable for postgraduate students and non-experts.
Additional Information
BISAC Categories:
- Mathematics | Matrices
- Mathematics | Probability & Statistics - General
Dewey: 512.943
LCCN: 2010275269
Series: London Mathematical Society Lecture Notes
Physical Information: 0.9" H x 5.9" W x 8.8" (1.40 lbs) 448 pages
 
Descriptions, Reviews, Etc.
Publisher Description:
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.

Contributor Bio(s): Blower, Gordon: - Gordon Blower is currently Head of the Department of Mathematics and Statistics at Lancaster University, and Professor of Mathematical Analysis.