29 citations · 67 across the 12 of their papers we have counts for
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math.OA2014★ 29 cited
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…
math.OA2014★ 2 cited
Regularity of Polynomials in Free Variables
I. Charlesworth, D. Shlyakhtenko
We show that the spectral measure of any non-commutative polynomial of a non-commutative -tuple cannot have atoms if the free entropy dimension of that -tuple is (see als…
math.OA2014★ 24 cited
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…