Free Probability Theory (Fields Institute Communications)

Free Probability Theory (Fields Institute Communications)

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Description

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.

Contents

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

Product Details

  • ISBN13: 9780821806753
  • Format: Hardback
  • Number Of Pages: 312
  • ID: 9780821806753
  • ISBN10: 0821806750

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