| Autor: |
Gu, Yinzheng, Skoufranis, Paul |
| Rok vydání: |
2016 |
| Předmět: |
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| Zdroj: |
International Mathematics Research Notices (2018), no. 23, 7359-7419 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1093/imrn/rnx104 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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