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arXiv · 1403.4907

On two-faced families of non-commutative random variables

Ian Charlesworth·Brent Nelson·Paul Skoufranis
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Abstract

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 partitions. These diagrams produce an operator model on a Fock space suitable for representing any two-faced family of non-commutative random variables. Furthermore, using a Kreweras complement on bi-non-crossing partitions we establish the expected formulas for the multiplicative convolution of a bi-free pair of two-faced families.

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Ian Charlesworth, Brent Nelson, Paul Skoufranis. 2014-03-19. On two-faced families of non-commutative random variables. https://doi.org/10.4153/cjm-2015-002-6

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