99 citations · 460 across the 54 of their papers we have counts for
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Random matrices, free probability, planar algebras and subfactors
A. Guionnet, V. F. R. Jones, D. Shlyakhtenko
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, na…
Lower estimates on microstates free entropy dimension
D. Shlyakhtenko
By proving that certain free stochastic differential equations have stationary solutions, we give a lower estimate on the microstates free entropy dimension of certain -tuples $…
Free diffusions and Matrix models with strictly convex interaction
A. Guionnet, D. Shlyakhtenko
We study solutions to the free stochastic differential equation $dX_t = dS_t - \half DV(X_t)dt$, where is a locally convex polynomial potential in non-commuting variables.…
On Classical Analogues of Free Entropy Dimension
A. Guionnet, D. Shlyakhtenko
We define a classical probability analogue of Voiculescu's free entropy dimension that we shall call the classical probability entropy dimension of a probability measure on $\mathb…