On Two-faced Families of Non-commutative Random Variables
Printed: Dec 2015
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
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.
free probability, operator algebras, bi-free
46L54 - Free probability and free operator algebras