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arXiv · 1708.05334

Bi-monotonic independence for pairs of algebras

Yinzheng Gu·Takahiro Hasebe·Paul Skoufranis
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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.

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Yinzheng Gu, Takahiro Hasebe, Paul Skoufranis. 2017-08-17. Bi-monotonic independence for pairs of algebras. https://arxiv.org/abs/1708.05334

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