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Communications in Mathematical Physics

, Volume 338, Issue 2, pp 801–847 | Cite as

Combinatorics of Bi-Freeness with Amalgamation

  • Ian Charlesworth
  • Brent Nelson
  • Paul Skoufranis
Article

Abstract

In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cumulants is necessary and sufficient for bi-free independence with amalgamation. Further, we develop a multiplicative convolution for operator-valued random variables and explore ways to construct bi-free pairs of B-faces.

Keywords

Probability Space Moment Function Multiplicative Function Free Probability Unital Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Ian Charlesworth
    • 1
  • Brent Nelson
    • 1
  • Paul Skoufranis
    • 2
  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA

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