This book presents the first comprehensive introduction to free probability theory, a highly noncommutative probability theory with independence based on free products instead of tensor products. Basic examples of this kind of theory are provided by convolution operators on free groups and by the asymptotic behavior of large Gaussian random matrices. The probabilistic approach to free products has led to a recent surge of new results on the von Neumann algebras of free groups. The book is ideally suited as a textbook for an advanced graduate course and could also provide material for a seminar. In addition to researchers and graduate students in mathematics, this book will be of interest to physicists and others who use random matrices.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Research mathematicians and advanced graduate students in operator algebras, noncommutative probability theory or random matrices.

Reviews

"Accessible to persons without any background in operator algebras ... recommended to everyone who wants to get an impression of the beauty and fruitfulness of the concept of freeness."

-- Mathematical Reviews

Table of Contents

• Free products
• Free random variables in noncommutative probability theory
• Free harmonic analysis
• Random matrices and asymptotic freeness
• Free product factors