32 citations · 185 across the 24 of their papers we have counts for
4 papers · 1 filter
Independences and Partial -Transforms in Bi-Free Probability
Paul Skoufranis
In this paper, we examine how various notions of independence in non-commutative probability theory arise in bi-free probability. We exhibit how Boolean and monotone independence o…
Combinatorics of Bi-Freeness with Amalgamation
Ian Charlesworth, Brent Nelson, Paul Skoufranis
In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cum…
Thompson's theorem for II_1 factors
Matthew Kennedy, Paul Skoufranis
A theorem of Thompson provides a non-self-adjoint variant of the classical Schur-Horn theorem by characterizing the possible diagonal values of a matrix with given singular values.…
On two-faced families of non-commutative random variables
Ian Charlesworth, Brent Nelson, Paul Skoufranis
We demonstrate that the notions of bi-free independence and combinatorial-bi-free independence of two-faced families are equivalent using a diagrammatic view of bi-non-crossing par…