114 citations · 114 across the 2 of their papers we have counts for
6 papers · 1 filter
On the structure of non-commutative white noises
Claus Köstler, Roland Speicher
We consider the concepts of continuous Bernoulli systems and non-commutative white noises. We address the question of isomorphism of continuous Bernoulli systems and show that for…
Second Order Freeness and Fluctuations of Random Matrices: II. Unitary Random Matrices
James A. Mingo, Piotr Sniady, Roland Speicher
We extend the relation between random matrices and free probability theory from the level of expectations to the level of fluctuations. We show how the concept of "second order fre…
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…
Free Calculus
Roland Speicher
I give a survey about my work on combinatorial and probabilistic aspects of free probability theory. In particular, I present the combinatorial description of freeness in terms of…
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…