Hidden Bibliographic Details
| ISBN: | 9781139127547
1139127543
9781139107129
1139107127
9780521133128
0521133122
9781139114714
1139114719
9781283295864
1283295865
1107203619
9781107203617
1139122622
9781139122627
9786613295866
6613295868
1139116886
9781139116886
|
|---|
| Notes: | Includes bibliographical references (pages 424-432) and index.
English.
Print version record.
|
|---|
| Summary: | 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.
|
|---|
| Other form: | Print version: Blower, G. (Gordon). Random matrices. Cambridge ; New York : Cambridge University Press, ©2009 9780521133128
|
|---|
