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...

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Bibliographische Detailangaben
1. Verfasser: Blower, G. (VerfasserIn)
Format: Elektronisch E-Book
Sprache:English
Veröffentlicht: Cambridge Cambridge University Press 2009
Schriftenreihe:London Mathematical Society lecture note series 367
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Online-Zugang:BSB01
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Zusammenfassung: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
Beschreibung:Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Beschreibung:1 online resource (x, 437 pages)
ISBN:9781139107129
DOI:10.1017/CBO9781139107129

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