Combinatorics of Bi-Freeness with Amalgamation

被引：0
|
作者：
Ian Charlesworth
Brent Nelson
Paul Skoufranis
机构：
[1] UCLA,Department of Mathematics
[2] Texas A&M University,Department of Mathematics
来源：
Communications in Mathematical Physics | 2015年 / 338卷
关键词：
Probability Space; Moment Function; Multiplicative Function; Free Probability; Unital Algebra;
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学科分类号：
摘要：
In this paper, we develop the theory of bi-freeness in an amalgamated setting. We construct the operator-valued bi-free cumulant functions, and show that the vanishing of mixed cumulants is necessary and sufficient for bi-free independence with amalgamation. Further, we develop a multiplicative convolution for operator-valued random variables and explore ways to construct bi-free pairs of B-faces.
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页码：801 / 847
页数：46
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