Abstract
By proving that certain free stochastic differential equations with analytic coefficients have stationary solutions, we give a lower estimate on the microstates free entropy dimension of certain -tuples . In particular, we show that , where and is the set of values of derivations with the property that . We show that for sufficiently small (depending on ) and a -semicircular family, . In particular, for small , -deformed free group factors have no Cartan subalgebras. An essential tool in our analysis is a free analog of an inequality between Wasserstein distance and Fisher information introduced by Otto and Villani (and also studied in the free case by Biane and Voiculescu).
Citation
Dimitri Shlyakhtenko. "Lower estimates on microstates free entropy dimension." Anal. PDE 2 (2) 119 - 146, 2009. https://doi.org/10.2140/apde.2009.2.119
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