74 citations · 142 across the 15 of their papers we have counts for
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math.OA2005★ 1 cited
A Free Analogue of Shannon's Problem on Monotonicity of Entropy
D. Shlyakhtenko
We prove a free probability analog of a result of Artstein-Bally-Barthez-Naor. In particualar we prove that if X_{1},X_{2},... are freely independent identically distributed random…
math.OA2005★ 5 cited
Notes on Free Probability Theory
Dimitri Shlyakhtenko
These notes are from a 4-lecture mini-course taught by the author at the conference on von Neumann algebras as part of the ``Geometrie non commutative en mathematiques et physique'…
math.OA2005
Remarks on free entropy dimension
Dimitri Shlyakhtenko
We prove a technical result, showing that the existence of a closable unbounded dual system in the sense of Voiculescu is equivalent to the finiteness of free Fisher information. T…