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# Free Probability Theory

### About this Title

**Dan-Virgil Voiculescu**, *University of California, Berkeley, Berkeley, CA*, Editor

Publication: Fields Institute Communications

Publication Year:
1997; Volume 12

ISBNs: 978-0-8218-0675-3 (print); 978-1-4704-2980-5 (online)

DOI: https://doi.org/10.1090/fic/012

MathSciNet review: MR1426832

MSC: Primary 46-06; Secondary 46Lxx

### Table of Contents

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**Front/Back Matter**

**Chapters**

- Philippe Biane – Free Brownian motion, free stochastic calculus, and random matrices
- Michael Douglas – Large $N$ quantum field theory and matrix models
- Ken Dykema – Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states
- Emmanuel Germain – Amalgamated free product $C^*$-algebras and $KK$-theory
- Ian Goulden and D Jackson – Connexion coefficients for the symmetric group, free products in operator algebras, and random matrices
- Uffe Haagerup – On Voiculescu’s $R$- and $S$-transforms for free noncommuting random variables
- Alexandru Nica and Roland Speicher – $R$-diagonal pairs—A common approach to Haar unitaries and circular elements
- Michael Pimsner – A class of $C^*$-algebras generalizing both Cuntz-Krieger algebras and crossed products by ${\mathbb Z}$
- Florin Radulescu – An invariant for subfactors in the von Neumann algebra of a free group
- Dimitri Shlyakhtenko – Limit distributions of matrices with bosonic and fermionic entries
- Dimitri Shlyakhtenko – $R$-transform of certain joint distributions
- Roland Speicher – On universal products
- Roland Speicher and Reza Woroudi – Boolean convolution
- Erling Stormer – States and shifts on infinite free products of $C$*-algebras
- Dan Voiculescu – The analogues of entropy and of Fisher’s information measure in free probability theory. IV: Maximum entropy and freeness
- A Zee – Universal correlation in random matrix theory: A brief introduction for mathematicians