| Autor: |
Gu, Yinzheng, Skoufranis, Paul |
| Rok vydání: |
2016 |
| Předmět: |
|
| Zdroj: |
Journal of Functional Analysis 273 (2017), no. 5, 1663-1733 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1016/j.jfa.2017.06.002 |
| Popis: |
In this paper, the notion of conditionally bi-free independence for pairs of algebras is introduced. The notion of conditional $(\ell, r)$-cumulants are introduced and it is demonstrated that conditionally bi-free independence is equivalent to mixed cumulants. Furthermore, limit theorems for the additive conditionally bi-free convolution are studied using both combinatorial and analytic techniques. In particular, a conditionally bi-free partial $\mathcal{R}$-transform is constructed and a conditionally bi-free analogue of the L\'{e}vy-Hin\v{c}in formula for planar Borel probability measures is derived. |
| Databáze: |
arXiv |
| Externí odkaz: |
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