18 citations · 41 across the 9 of their papers we have counts for
19 papers · 1 filter
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…
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'…
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…
The Microstates Free Entropy Dimension of any DT--operator is 2
Ken Dykema, Kenley Jung, Dimitri Shlyakhtenko
Suppose that μis an arbitrary Borel measure on the complex plane with compact support and take c > 0. If Z is a DT(μ,c)-operator as defined by Dykema and Haagerup, then the microst…
Non-microstates free entropy dimension for groups
I. Mineyev, D. Shlyakhtenko
We show that for any discrete finitely-generated group G and any self-adjoint n-tuple X_1,...,X_n of generators of the group algebra of G, Voiculescu's non-microstates free entropy…
L^2-Homology for von Neumann Algebras
Alain Connes, Dimitri Shlyakhtenko
We define the notion of L^2 homology and L^2 Betti numbers for a tracial von Neumann algebra, or, more generally, for any involutive algebra with a trace. The definition of these i…