4 papers
Operator-valued distributions: I. Characterizations of freeness
Alexandru Nica, Dimitri Shlyakhtenko, Roland Speicher
Let be a -probability space. Assume that itself is a -probability space; then can be viewed as -probability space as well. Let be in . We look at the qu…
R-cyclic families of matrices in free probability
Alexandru Nica, Dimitri Shlyakhtenko, Roland Speicher
We introduce the concept of ``R-cyclic family'' of matrices with entries in a non-commutative probability space; the definition consists in asking that only the ``cyclic'' non-cros…
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…
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…