A Combinatorial Approach to Voiculescu's Bi-Free Partial Transforms

Abstract

In this paper, we present a combinatorial approach to the 2-variable bi-free partial $S$- and $T$-transforms recently discovered by Voiculescu. This approach produces an alternate definition of said transforms using $(\ell ,r)$-cumulants.

References in corpus (4)

• Free Probability for Pairs of Faces I
• Combinatorics of Bi-Freeness with Amalgamation
• Double-ended queues and joint moments of left-right canonical operators on full Fock space
• On two-faced families of non-commutative random variables

Cited by in corpus (1)

• On Operator-Valued Bi-Free Distributions