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arXiv · 1408.3251

Combinatorics of Bi-Freeness with Amalgamation

Ian Charlesworth·Brent Nelson·Paul Skoufranis
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Abstract

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 cumulants is necessary and sufficient for bi-free independence. Further, we develop a multiplicative convolution for operator-valued random variables and explore ways to construct bi-free pairs of B-faces.

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BibTeXRIS

Ian Charlesworth, Brent Nelson, Paul Skoufranis. 2014-08-14. Combinatorics of Bi-Freeness with Amalgamation. https://doi.org/10.1007/s00220-015-2326-8

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