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arXiv · 1609.07820

Conditionally Bi-Free Independence with Amalgamation

Yinzheng Gu·Paul Skoufranis
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Abstract

In this paper, we introduce the notion of conditionally bi-free independence in an amalgamated setting. We define operator-valued conditionally bi-multiplicative pairs of functions and construct operator-valued conditionally bi-free moment and cumulant functions. It is demonstrated that conditionally bi-free independence with amalgamation is equivalent to the vanishing of mixed operator-valued bi-free and conditionally bi-free cumulants. Furthermore, an operator-valued conditionally bi-free partial $\mathcal{R}$-transform is constructed and various operator-valued conditionally bi-free limit theorems are studied.

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Yinzheng Gu, Paul Skoufranis. 2016-09-26. Conditionally Bi-Free Independence with Amalgamation. https://doi.org/10.1093/imrn%2Frnx104

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