Random Matrices: High Dimensional Phenomena: 367 (London Mathematical Society Lecture Note Series, Series Number 367) - Softcover

Book 302 of 387: London Mathematical Society Lecture Notes

Blower, Gordon

 
9780521133128: Random Matrices: High Dimensional Phenomena: 367 (London Mathematical Society Lecture Note Series, Series Number 367)
Softcover
ISBN 10: 0521133122 ISBN 13: 9780521133128
Publisher: Cambridge University Press, 2009

Synopsis

This book focuses on the behaviour 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.

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About the Author

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

"About this title" may belong to another edition of this title.

Publisher
Cambridge University Press
Publication date
2009
Language
English
ISBN 10 
0521133122
ISBN 13 
9780521133128
Binding
Paperback
Edition number
1
Number of pages
448