Roland Speicher
Published 2009-10-31Version 1
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.
Comments: 21 pages; my contribution for the Handbook on Random Matrix Theory, to be published by Oxford University Press
Self-normalized Sums in Free Probability Theory
Cumulant-cumulant relations in free probability theory from Magnus' expansion
Local limit theorems in free probability theory
![QR code for arXiv:0911.0087 [math.PR]](http://oss.arxitics.com/images/favicon.svg)