Random matrices, free probability, planar algebras and subfactors
Operator Algebras
2008-07-08 v2
Abstract
Using a family of graded algebra structures on a planar algebra and a family of traces coming from random matrix theory, we obtain a tower of non-commutative probability spaces, naturally associated to a given planar algebra. The associated von Neumann algebras are II factors whose inclusions realize the given planar algebra as a system of higher relative commutants. We thus give an alternative proof to a result of Popa that every planar algebra can be realized by a subfactor.
Cite
@article{arxiv.0712.2904,
title = {Random matrices, free probability, planar algebras and subfactors},
author = {A. Guionnet and V. F. R. Jones and D. Shlyakhtenko},
journal= {arXiv preprint arXiv:0712.2904},
year = {2008}
}
Comments
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