Decompositions of the free additive convolution
Decompositions of the free additive convolution
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自由加性卷积的分解
DOI：
10.1016/j.jfa.2007.01.010
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发表时间：
2006
影响因子：
1.7
通讯作者：
R. Lenczewski
中科院分区：
文献类型：
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作者：
R. Lenczewski
我们引入并研究了一类新的概率测度卷积，记为μν，称为s-自由加性卷积，它是由与自由加性卷积相关的从属函数定义的.对于紧支撑的μ和ν，我们使用另一种称为正交加性卷积的卷积导出μν的交替分解。这种分解导致自由加性卷积μ π ν的两种类型的“完全”交替分解。更重要的是，我们开发了一个可操作的方法从属属性，并介绍了相关的概念的s-自由独立。此外，我们建立卷积与非交换独立（自由，单调和布尔）的主要概念之间的关系。最后，我们的结果导致自然分解的自由产品的根图。
We introduce and study a new type of convolution of probability measures, denoted μν and called the s-free additive convolution, which is defined by the subordination functions associated with the free additive convolution. We derive an alternating decomposition of μν for compactly supported μ and ν, using another convolution called orthogonal additive convolution. This decomposition leads to two types of ‘complete’ alternating decompositions of the free additive convolution μ⊞ν. More importantly, we develop an operatorial approach to the subordination property and introduce the associated notion of s-free independence. Moreover, we establish relations between convolutions associated with the main notions of noncommutative independence (free, monotone and boolean). Finally, our result leads to natural decompositions of the free product of rooted graphs.