Random Matrices

High Dimensional Phenomena

Gordon Blower (Lancaster University)

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English

Cambridge University Press
08 October 2009

Algebra; Probability & statistics

Series: London Mathematical Society Lecture Note Series

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.

By: Gordon Blower (Lancaster University)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 367
Dimensions: Height: 228mm, Width: 150mm, Spine: 22mm
Weight: 630g
ISBN: 9780521133128
ISBN 10: 0521133122
Series: London Mathematical Society Lecture Note Series
Pages: 448
Publication Date: 08 October 2009
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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

Reviews for Random Matrices: High Dimensional Phenomena

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