Free Probability Theory: Random Matrices and von Neumann Algebras

Dan Voiculescu
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Dan Voiculescu: University of California, Department of Mathematics

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 227-242 from Springer

Abstract: 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 ℤ n 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.

Date: 1995
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DOI: 10.1007/978-3-0348-9078-6_17

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