Wow! eBook
The Semicircle Law, Free Random Variables and Entropy
Author(s): Fumio Hiai (Author), Petz Denes (Author)
- Publisher: American Mathematical Society
- Publication Date: 4 Jan. 2007
- Language: English
- Print length: 376 pages
- ISBN-10: 0821841351
- ISBN-13: 9780821841358
Book Description
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.
