Mathematical Surveys and Monographs 2000; 376 pp; softcover Volume: 77 ISBN10: 0821841351 ISBN13: 9780821841358 List Price: US$98 Member Price: US$78.40 Order Code: SURV/77.S
 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. Table of Contents  Overview
 Probability laws and noncommutative random variables
 The free relation
 Analytic function theory and infinitely divisible laws
 Random matrices and asymptotically free relation
 Large deviations for random matrices
 Free entropy of noncommutative random variables
 Relation to operator algebras
 Bibliography
 Index
