Geodesic
On Two-faced Families of Non-commutative Random Variables
Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1290-1325

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CJM-2015-002-6
Mots-clés : 46L54, free probability, operator algebras, bi-free 
Charlesworth, Ian; Nelson, Brent; Skoufranis, Paul. On Two-faced Families of Non-commutative Random Variables. Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1290-1325. doi: 10.4153/CJM-2015-002-6
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