Combinatorics of Bi-Freeness with Amalgamation

被引：25

作者：

Charlesworth, Ian ^{[1
]}

Nelson, Brent ^{[1
]}

Skoufranis, Paul ^{[2
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2015年 / 338卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Probability Space; Moment Function; Multiplicative Function; Free Probability; Unital Algebra;

D O I：

10.1007/s00220-015-2326-8

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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.

引用

页码：801 / 847

页数：47

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