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Free Probability Theory: Random Matrices and von Neumann Algebras

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Proceedings of the International Congress of Mathematicians

Abstract

Independence in usual noncommutative probability theory (or in quantum physics) is based on tensor products. This lecture is about what happens if tensor products are replaced by free products. The theory one obtains is highly noncommutative: freely independent random variables do not commute in general. Also, at the level of groups, this means instead of ℤn we will consider the noncommutative free group F(n) = ℤ* ⋯ *ℤ or, looking at the Cayler graphs, a lattice is replaced by a homogeneous tree.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA, 94720, USA

    Dan Voiculescu

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  1. Dan Voiculescu
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Editor information

Editors and Affiliations

  1. Département de Mathématiques, EPFL, 1015, Laussane, Switzerland

    S. D. Chatterji

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© 1995 Birkhäser Verlag, Basel, Switzerland

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Voiculescu, D. (1995). Free Probability Theory: Random Matrices and von Neumann Algebras. In: Chatterji, S.D. (eds) Proceedings of the International Congress of Mathematicians. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-9078-6_17

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  • DOI: https://doi.org/10.1007/978-3-0348-9078-6_17

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9897-3

  • Online ISBN: 978-3-0348-9078-6

  • eBook Packages: Springer Book Archive

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