Random matrices, free probability, planar algebras and subfactors

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dc.creatorGuionnet, A.
dc.creatorJones, V. F. R.
dc.creatorShlyakhtenko, D.
dc.date2007-12-18
dc.date2008-07-08
dc.date.accessioned2026-07-07T09:48:31Z
dc.date.available2026-07-07T09:48:31Z
dc.descriptionUsing 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$_{1}$ 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.
dc.descriptionMinor changes
dc.identifierhttps://arxiv.org/abs/0712.2904
dc.identifierhttp://arxiv.org/abs/0712.2904
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164243
dc.subjectOperator Algebras
dc.subject46L37; 46L54; 15A52
dc.titleRandom matrices, free probability, planar algebras and subfactors
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