ENGLISH

The semicircle law, free random variables, and entropy

By Fumio Hiai and Denes Petz

Book information

Publisher
American Mathematical Society
Year
2006
ISBN
9780821841358, 9780821820810, 0821841351, 0821820818
ISSN
0076-5376
Open Library ID
OL9461012M
Language
english
Format
DJVU
Filesize
3 MB (2823319 bytes)
Series
Mathematical surveys and monographs 77
Pages
381\381
Time added
2010-05-31 15:29:46
Математика;Теория вероятностей и математическая ст

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.

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