The Semicircle Law, Free Random Variables and Entropy (Mathematical Surveys & Monographs)

Hiai, Fumio/ Petz, Denes

ISBN 10: 0821841351 / ISBN 13: 9780821841358

Published by Amer Mathematical Society, 2006

About this Item

376 pages. 9.75x7.00x1.00 inches. In Stock.

Seller Inventory # __0821841351

Bibliographic Details

• Title: The Semicircle Law, Free Random Variables and Entropy (Mathematical Surveys & Monographs)
• Publisher: Amer Mathematical Society
• Publication Date: 2006
• Language: English
• ISBN 10: 0821841351
• ISBN 13: 9780821841358
• Binding: Paperback
• Condition: Brand New
• Weight: 0.7 kilograms

About this title

Synopsis

The book treats free probability theory, which has been extensively developed since the early 1980s. The emphasis is put on entropy and the random matrix model approach. The volume 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 the book is the parallelism between the normal and semicircle laws. Voiculescu's multivariate free entropy theory is presented with full proofs and extends the results to unitary operators. Some applications to operator algebras are also given. Based on lectures given by the authors in Hungary, Japan, and Italy, the book is a good reference for mathematicians interested in free probability theory and can serve as a text for an advanced graduate course.