**Fields Institute Communications**

Volume: 12;
1997;
312 pp;
Hardcover

MSC: Primary 46;
Secondary 47; 05; 81

Print ISBN: 978-0-8218-0675-3

Product Code: FIC/12

List Price: $101.00

AMS Member Price: $80.80

MAA Member Price: $90.90

**Electronic ISBN: 978-1-4704-2980-5
Product Code: FIC/12.E**

List Price: $101.00

AMS Member Price: $80.80

MAA Member Price: $90.90

# Free Probability Theory

Share this page *Edited by *
*Dan-Virgil Voiculescu*

A co-publication of the AMS and Fields Institute

Free probability theory is a highly noncommutative
probability theory, with independence based on free products instead
of tensor products. The theory models random matrices in the large
\(N\)
limit and operator algebra free products. It has led to a
surge of new results on the von Neumann algebras of free groups.

This is a volume of papers from a workshop on Random Matrices and
Operator Algebra Free Products, held at The Fields Institute for
Research in the Mathematical Sciences in March 1995. Over the last few
years, there has been much progress on the operator algebra and
noncommutative probability sides of the subject. New links with the
physics of masterfields and the combinatorics of noncrossing
partitions have emerged. Moreover there is a growing free entropy
theory. The idea of this workshop was to bring together people working
in all these directions and from an even broader free products area
where future developments might lead.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

#### Readership

Graduate students, research mathematicians, mathematical physicists, and theoretical physicists interested in operator algebras, noncommutative probability theory or random matrix models.

# Table of Contents

## Free Probability Theory

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Free Brownian motion, free stochastic calculus, and random matrices 110
- Large 𝑁 quantum field theory and matrix models 2130
- Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states 4150
- Amalgamated free product 𝐶*-algebras and 𝐾𝐾-theory 8998
- Connexion coefficients for the symmetric group, free products in operator algebras, and random matrices 105114
- On Voiculescu’s 𝑅- and 𝑆-transforms for free noncommuting random variables 127136
- 𝑅-diagonal pairs—A common approach to Haar unitaries and circular elements 149158
- A class of 𝐶*-algebras generalizing both Cuntz-Krieger algebras and crossed products by ℤ 189198
- An invariant for subfactors in the von Neumann algebra of a free group 213222
- Limit distributions of matrices with bosonic and fermionic entries 241250
- 𝑅-transform of certain joint distributions 253262
- On universal products 257266
- Boolean convolution 267276
- States and shifts on infinite free products of 𝐶*-algebras 281290
- The analogues of entropy and of Fisher’s information measure in free probability theory. IV: Maximum entropy and freeness 293302
- Universal correlation in random matrix theory: A brief introduction for mathematicians 303312
- Back Cover Back Cover1322