Conditionally bi-free independence for pairs of faces☆
Conditionally bi-free independence for pairs of faces☆
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有条件双自由独立双脸☆
DOI：
10.1016/j.jfa.2017.06.002
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发表时间：
2016
影响因子：
1.7
通讯作者：
P. Skoufranis
中科院分区：
文献类型：
--
作者：
Yinzheng Gu;P. Skoufranis
本文引入了面对条件双自由独立性的概念。引入了条件（ε，r）-累积量的概念，证明了条件双自由独立性等价于混合累积量的消失。此外，利用组合和分析技巧研究了可加条件双自由卷积的极限定理。特别地，构造了一个条件双自由的部分R变换，并导出了平面Borel概率测度的Lévy-Hinčin公式的条件双自由模拟.
In this paper, the notion of conditionally bi-free independence for pairs of faces is introduced. The notion of conditional (ℓ, r)-cumulants is introduced and it is demonstrated that conditionally bi-free independence is equivalent to the vanishing of 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 R-transform is constructed and a conditionally bi-free analogue of the Lévy–Hinčin formula for planar Borel probability measures is derived.