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Random matrices : high dimensional phenomena /
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
2009.
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| Colección: | London Mathematical Society lecture note series ;
367. |
| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | 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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| Descripción Física: | 1 online resource (x, 437 pages) |
| Bibliografía: | Includes bibliographical references (pages 424-432) and index. |
| ISBN: | 9781139127547 1139127543 9781139107129 1139107127 1107203619 9781107203617 1139122622 9781139122627 9786613295866 6613295868 1139116886 9781139116886 |