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Free probability theory

Author: D V Voiculescu
Publisher: Providence, RI : American Mathematical Society, 1997.
Series: Fields Institute communications, v. 12.
Edition/Format:   eBook : Document : Conference publication : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Conference papers and proceedings
Electronic books
Congresses
Additional Physical Format: Print version:
Voiculescu, Dan-Virgil
Free Probability Theory
Providence : American Mathematical Society,c1996
Material Type: Conference publication, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: D V Voiculescu
ISBN: 0821806750 9780821806753 9781470429805 1470429802
OCLC Number: 956663964
Notes: Papers from a workshop on random matrices and operator algebra free products held Mar. 1995 at the Fields Institute.
Description: 1 online resource.
Contents: Free Brownian motion, free stochastic calculus, and random matrices Large $N$ quantum field theory and matrix models Free products of finite dimensional and other von Neumann algebras with respect to non-tracial states Amalgamated free product $C^*$-algebras and $KK$-theory Connexion coefficients for the symmetric group, free products in operator algebras, and random matrices On Voiculescu's $R$- and $S$-transforms for free noncommuting random variables $R$-diagonal pairs --
A common approach to Haar unitaries and circular elements A class of $C^*$-algebras generalizing both Cuntz-Krieger algebras and crossed products by ${\mathbb Z}$ An invariant for subfactors in the von Neumann algebra of a free group Limit distributions of matrices with bosonic and fermionic entries $R$-transform of certain joint distributions On universal products Boolean convolution States and shifts on infinite free products of $C$*-algebras The analogues of entropy and of Fisher's information measure in free probability theory. IV: Maximum entropy and freeness Universal correlation in random matrix theory: A brief introduction for mathematicians.
Series Title: Fields Institute communications, v. 12.
Responsibility: Dan-Virgil Voiculescu, editor.

Abstract:

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 probabi.

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