Random Matrices: High Dimensional Phenomena (London Mathematical Society Lecture Note Series)

Gordon Blower

ISBN 10: 0521133122 / ISBN 13: 9780521133128

Published by Cambridge University Press 2009-10-08, 2009

About this Item

Seller Inventory # 6666-IUK-9780521133128

Bibliographic Details

• Title: Random Matrices: High Dimensional Phenomena (London Mathematical Society Lecture Note Series)
• Publisher: Cambridge University Press 2009-10-08
• Publication Date: 2009
• Language: English
• ISBN 10: 0521133122
• ISBN 13: 9780521133128
• Binding: Paperback
• Condition: New

About this title

Synopsis

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.

About the Author

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