Associative convolutions arising from conditionally free convolution

Krystek AD; Wojakowski LJ

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Associative convolutions arising from conditionally free convolution

机译：有条件自由卷积引起的联想卷积

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摘要

We define two families of deformations of probability measures depending on the second free cumulants and the corresponding new associative convolutions arising from the conditionally free convolution. These deformations do not commute with dilation of measures, which means that the limit theorems cannot be obtained as a direct application of the theorems for the conditionally free case. We calculate the general form of the central and Poisson limit theorems. We also find the explicit form for three important examples.

机译：我们根据第二个自由累积量和有条件的自由卷积产生的相应的新联想卷积，定义了概率测度的两个变形家族。这些变形不随测度的扩张而变化，这意味着不能将极限定理直接用作无条件情况下的定理。我们计算中心定理和泊松极限定理的一般形式。我们还找到了三个重要示例的显式形式。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2005年第3期|共31页
作者
Krystek AD; Wojakowski LJ;
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正文语种 eng
中图分类物理学;
关键词
convolution; conditionally free; deformations; moment-cumulant formulae; limit theorems; THEOREMS;

机译：卷积;条件自由;变形;矩累积量公式;极限定理;定理;

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专利

1. Associative convolutions arising from conditionally free convolution [J] . Krystek AD, Wojakowski LJ Infinite dimensional analysis, quantum probability, and related topics . 2005,第3期

机译：有条件自由卷积引起的联想卷积
2. Limit Theorems for Additive Conditionally Free Convolution [J] . Jiun-Chau Wang Canadian Journal of Mathematics . 2011,第1期

机译：可加条件自由卷积的极限定理
3. ON MULTIPLICATIVE CONDITIONALLY FREE CONVOLUTION [J] . MIHAI POPA, JIUN-CHAU WANG Transactions of the American Mathematical Society . 2011,第12期

机译：关于乘法有条件的自由卷积
4. Image Semantic Segmentation Using Deep Convolutional Nets, Fully Connected Conditional Random Fields, and Dilated Convolution [C] . Degui Xiao, Pei Zhong IEEE International Conference on High Performance Computing and Communications;IEEE International Conference on Smart City;IEEE International Conference on Data Science and Systems . 2019

机译：使用深度卷积网络，完全连接的条件随机场和膨胀卷积的图像语义分割
5. Analysing the effects of data augmentation and free parameters for text classification with recurrent convolutional neural networks. [D] . Quijas, Jonathan K. 2017

机译：使用递归卷积神经网络分析数据扩充和自由参数对文本分类的影响。
6. Measurement of Conditional Relatedness Between Genes Using Fully Convolutional Neural Network [O] . Yan Wang, Shuangquan Zhang, Lili Yang, 2019

机译：使用全卷积神经网络测量基因之间的条件相关性
7. Associative convolutions arising from conditionally free convolution [O] . Anna Krystek, Łukasz Wojakowski 2014

机译：由有条件自由卷积产生的联想卷积
8. Numerical Evaluation of the 'Dual-Kernel Counter-flow' Matric Convolution Integral that Arises in Discrete/Continuous (D/C) Control Theory [R] . Nixon, D. D. 2009

机译：离散/连续（D / C）控制理论中“双核逆流”基质卷积积分的数值计算

Associative convolutions arising from conditionally free convolution

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