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Random Matrices, Free Probability, Planar Algebras and Subfactors by Guionnet, A.; Jones, V. F. R.; Shlyakhtenko, D. is a scholarly article available to read on EtoBox.

What is Random Matrices, Free Probability, Planar Algebras and Subfactors about?

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.

Author

Guionnet, A.; Jones, V. F. R.; Shlyakhtenko, D.

Published

2007

Language

EN