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math.OA1998★ 1 cited
A Microstates Approach to Relative Free Entropy
Dimitri Shlyakhtenko
We define and study a relative free entropy quantity, analogous in its properties to Voiculescu's relative free entropy Chi^*(...:B). Our definition uses matricial microstates, unl…
math.OA1998
Maximality of the microstates free entropy for R-diagonal elements
A. Nica, D. Shlyakhtenko, R. Speicher
A non-commutative non-selfadjoint random variable z is called R-diagonal, if its *-distribution is invariant under multiplication by free unitaries: if a unitary w is *-free from z…
math.OA1998★ 1 cited
Some minimization problems for the free analogue of the Fisher information
A. Nica, D. Shlyakhtenko, R. Speicher
We consider the free non-commutative analogue Phi^*, introduced by D. Voiculescu, of the concept of Fisher information for random variables. We determine the minimal possible value…