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Bi-monotonic Independence for Pairs of Algebras

Author

Listed:
  • Yinzheng Gu

    (Queen’s University)

  • Takahiro Hasebe

    (Hokkaido University)

  • Paul Skoufranis

    (York University)

Abstract

In this article, the notion of bi-monotonic independence is introduced as an extension of monotonic independence to the two-faced framework for a family of pairs of algebras in a non-commutative space. The associated cumulants are defined, and a moment-cumulant formula is derived in the bi-monotonic setting. In general, the bi-monotonic product of states is not a state and the bi-monotonic convolution of probability measures on the plane is not a probability measure. This provides an additional example of how positivity need not be preserved under conditional bi-free convolutions.

Suggested Citation

  • Yinzheng Gu & Takahiro Hasebe & Paul Skoufranis, 2020. "Bi-monotonic Independence for Pairs of Algebras," Journal of Theoretical Probability, Springer, vol. 33(1), pages 533-566, March.
    • Handle: RePEc:spr:jotpro:v:33:y:2020:i:1:d:10.1007_s10959-019-00884-2
    DOI: 10.1007/s10959-019-00884-2
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