A Free Stochastic Partial Differential Equation

Details A Free Stochastic Partial Differential Equation A Free Stochastic Partial Differential Equation

2010-08-27

arxiv.org/abs/1008.4742v2

Mathematics

Operator Algebras

79 pages, important revision with new applications to q-Gaussian factors and improved exposition

Scientific paper

We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming also R^\omega\ embeddability. This includes an N-tuple of q-Gaussian random variables e.g. for |q|N\leq 0.13. More generally for |q|N<1 and |q|N^{1/2}\leq 0.13 we prove they still have microstate free entropy dimension N.

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