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Free Probability Theory
Edited by: Dan Voiculescu, University of California, Berkeley, CA
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
1997; 312 pp; hardcover
Volume: 12
ISBN-10: 0-8218-0675-0
ISBN-13: 978-0-8218-0675-3
List Price: US$96
Member Price: US$76.80
Order Code: FIC/12
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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

  • P. Biane -- Free Brownian motion, free stochastic calculus, and random matrices
  • M. R. Douglas -- Large \(N\) quantum field theory and matrix models
  • K. Dykema -- Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states
  • E. C. Germain -- Amalgamated free product \(C^*\)-algebras and \(KK\)-theory
  • I. P. Goulden and D. M. Jackson -- Connexion coefficients for the symmetric group, free products in operator algebras, and random matrices
  • U. Haagerup -- On Voiculescu's \(R\)- and \(S\)-transforms for free noncommuting random variables
  • A. M. Nica and R. Speicher -- \(R\)-diagonal pairs--A common approach to Haar unitaries and circular elements
  • M. V. Pimsner -- A class of \(C\)*-algebras generalizing both Cuntz-Krieger algebras and crossed products by\({\mathbb Z}\)
  • F. Radulescu -- An invariant for subfactors in the von Neumann algebra of a free group
  • D. Y. Shlyakhtenko -- Limit distributions of matrices with bosonic and fermionic entries
  • D. Y. Shlyakhtenko -- \(R\)-transform of certain joint distributions
  • R. Speicher -- On universal products
  • R. Speicher and R. Woroudi -- Boolean convolution
  • E. Stormer -- States and shifts on infinite free products of \(C\)*-algebras
  • D. 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
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