Free Diffusions and Property AO
Abstract
We consider von Neumann algebras generated by the stationary laws of free stochastic differential equations of the form dXt = dSt -1/2 DV(Xt) for a suitably convex multivariate noncommutative polynomial V. Using techniques of Guionnet and Shlyakhtenko, we prove that these von Neumann algebras have property AO of Ozawa and are thus solid.
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