Conditionally monotone independence and the associated products of graphs

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Conditionally monotone independence and the associated products of graphs

机译：有条件的单调独立和相关产品的图表

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We reduce the conditionally monotone (c-monotone) independence of Hasebe to tensor independence on suitably constructed larger algebras. For that purpose, we use the approach developed for a reduction of similar type for boolean, free and monotone independences. We apply the tensor product realization of c-monotone random variables to introduce the c-comb (loop) product of birooted graphs, a generalization of the comb (loop) product of rooted graphs, and we show that it is related to the c-monotone additive (multiplicative) convolution of distributions.

机译：我们减少了有条件的单调（C-单调）独立于挥霍独立于适当地构建的较大代数。为此目的，我们使用开发的方法来减少Boolean，免费和单调独立。我们应用C-单调随机变量的张量产品实现，介绍Biroouted图的C-Comb（环）产品，梳理图的泛型（环路）产品，我们表明它与C-相关单调添加剂（乘法）分布卷积。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2019年第4期|共24页
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正文语种 eng
中图分类物理学;
关键词
Monotone independence; conditionally monotone independence; tensor independence; comb product of graphs; c-comb product of graphs;

机译：单调独立;有条件的单调独立;张量独立;梳理图形;图形的C梳状产品;

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专利

1. Conditionally monotone independence and the associated products of graphs [J] . Infinite dimensional analysis, quantum probability, and related topics . 2019,第4期

机译：有条件的单调独立和相关产品的图表
2. Conditionally monotone independence i: Independence, additive convolutions and related convolutions [J] . Hasebe T. Infinite dimensional analysis, quantum probability, and related topics . 2011,第3期

机译：有条件的单调独立性i：独立性，加性卷积和相关卷积
3. Conditionally Monotone Independence II: Multiplicative Convolutions and Infinite Divisibility [J] . Hasebe T. Complex analysis and operator theory . 2013,第1期

机译：有条件的单调独立性II：乘法卷积和无限除数
4. Conditional Products: An Alternative Approach to Conditional Independence [C] . A. P. Dawid, M. Studeny The Seventh International Workshop on Artificial Intelligence and Statistics Jan 3-6, 1999 Fort Lauderdale, Florida . 1999

机译：条件产品：条件独立的另一种方法
5. Travel time estimation and short-term prediction in urban arterial networks using conditional independence graphs and state-space neural networks. [D] . Singh, Ajay Kumar. 2006

机译：使用条件独立图和状态空间神经网络的城市动脉网络旅行时间估计和短期预测。
6. Estimation of graphical models whose conditional independence graphs are interval graphs and its application to modeling linkage disequilibrium [O] . Alun Thomas -1

机译：估计其条件独立性图是间隔图的图形模型及其在建模联动不平衡的应用
7. Conditionally monotone independence and the associated products of graphs [O] . Romuald Lenczewski 2019

机译：有条件的单调独立和图表的相关产品

Conditionally monotone independence and the associated products of graphs

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