Free Probability for Pairs of Faces I
arXiv:1306.6082 · doi:10.1007/s00220-014-2060-7
Abstract
We consider a notion of bi-freeness for systems of non-commutative random variables with two faces, one of left variables and another of right variables. This includes bi-free convolution operations, bi-free cumulants and the bi-free central limit.
33 pages
References in corpus (1)
Cited by in corpus (34)
- 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
- Conditionally Bi-Free Independence for Pairs of Algebras
- Fock space associated to Coxeter group of type B
- On Operator-Valued Bi-Free Distributions
- Independences and Partial -Transforms in Bi-Free Probability
- Bimonotone Brownian Motion
- An Operad of Non-commutative Independences Defined by Trees
- A Combinatorial Approach to Voiculescu's Bi-Free Partial Transforms
- An alternating moment condition for bi-freeness
- Bi-Boolean independence for pairs of algebras
- Preservation of algebraicity in free probability
- Towards a Classification of Multi-Faced Independence: A Representation-Theoretic Approach
- Bi-monotonic independence for pairs of algebras
- Free-free-Boolean independence for triples of algebras
- Free Probability for Pairs of Faces IV: Bi-free Extremes in the Plane
- Free-Boolean independence for pairs of algebras
- Conditionally Bi-Free Independence with Amalgamation
- Schoenberg correspondence for multifaced independence
- A Combinatorial Approach to the Opposite Bi-Free Partial -Transform
- An operator that relates to semi-meander polynomials via a two-sided q-Wick formula
- Analogues of Entropy in Bi-Free Probability Theory: Microstates
- Limit Theorems and Wrapping Transforms in Bi-free Probability Theory
- On Bi-R-Diagonal Pairs of Operators
- BMT Independence
- Principal functions for bi-free central limit distributions
- Multipartite rational functions
- Limit theorems in bi-free probability theory
- Lecture Notes on "Non-Commutative Distributions"
- Relations between convolutions and transforms in operator-valued free probability
- Bi-Free Entropy with Respect to Completely Positive Maps
- Free-Boolean independence with amalgamation
- Analytic aspects of the bi-free partial R-transform