R. Speicher. (2009)cite arxiv:0911.0087Comment: 21 pages; my contribution for the Handbook on Random Matrix Theory, to be published by Oxford University Press.
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.
%0 Journal Article
%1 speicher2009probability
%A Speicher, Roland
%D 2009
%K probability theory
%T Free Probability Theory
%U http://arxiv.org/abs/0911.0087
%X 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.
@article{speicher2009probability,
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.},
added-at = {2020-02-06T15:16:39.000+0100},
author = {Speicher, Roland},
biburl = {https://www.bibsonomy.org/bibtex/281ae1c171701d299d59775b1c9802252/kirk86},
description = {[0911.0087] Free Probability Theory},
interhash = {ed6e2fed5ea11f04b854ab3939b95f0a},
intrahash = {81ae1c171701d299d59775b1c9802252},
keywords = {probability theory},
note = {cite arxiv:0911.0087Comment: 21 pages; my contribution for the Handbook on Random Matrix Theory, to be published by Oxford University Press},
timestamp = {2020-02-06T15:24:48.000+0100},
title = {Free Probability Theory},
url = {http://arxiv.org/abs/0911.0087},
year = 2009
}