Random matrices, free probability, planar algebras and subfactors

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${}_1$ 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.

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References in corpus (1)

• Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices

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