The Semicircle Law, Free Random Variables and Entropy
American Mathematical Society (Publisher)
Published on 1. January 2000
Book
Hardback
386 pages
978-0-8218-2081-0 (ISBN)
Description
The book treats free probability theory, which has been extensively developed since the early eighties. The emphasis is put on entropy and the random matrix model approach. It is a unique presentation demonstrating the extensive interrelation between the topics. Wigner's theorem and its broad generalizations, such as asymptotic freeness of independent matrices, are explained in detail. Consistent throughout is the parallelism between the normal and semicircle laws. The authors present Voiculescu's multivariate free entropy theory with full proofs and extend the results to unitary operators. Some applications to operator algebras are also given. The book is the first essentially full-scale presentation on free probability theory and includes improvements of results and proofs in current literature. The combinatorial aspects of the specialized topics are emphasized; many examples are given. The book would be a suitable text for graduate courses in free probability theory.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
College/higher education
Professional and scholarly
Dimensions
Height: 260 mm
Width: 184 mm
Weight
903 gr
ISBN-13
978-0-8218-2081-0 (9780821820810)
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Schweitzer Classification