This is an announcement for the paper "Free probability theory" by Roland Speicher.

Abstract: Free probability theory was created by Dan Voiculescu around 1985, motivated by his efforts to understand special classes of von Neumann algebras. His discovery in 1991 that also random matrices satisfy asymptotically the freeness relation transformed the theory dramatically. Not only did this yield spectacular results about the structure of operator algebras, but it also brought new concepts and tools into the realm of random matrix theory. In the following we will give, mostly from the random matrix point of view, a survey on some of the basic ideas and results of free probability theory.

Archive classification: math.PR math.OA

Remarks: 21 pages; my contribution for the Handbook on Random Matrix Theory, to be published by Oxford University Press

The source file(s), RMT-chapter22.tex: 56575 bytes wignerpluswishart.ps: 11793 bytes wisharttimeswishart.ps: 10691 bytes, is(are) stored in gzipped form as 0911.0087.tar.gz with size 23kb. The corresponding postcript file has gzipped size 119kb.

Submitted from: speicher@mast.queensu.ca

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http://front.math.ucdavis.edu/0911.0087

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http://arXiv.org/abs/0911.0087

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