| 算子值半圆分布及其渐进自由矩阵模型 |
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| 引用本文： | 孟彬,郭懋正. 算子值半圆分布及其渐进自由矩阵模型[J]. 数学研究及应用, 2008, 28(4): 759-768 |
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| 作者姓名： | 孟彬 郭懋正 |
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| 作者单位： | 南京航空航天大学数学系,江苏 南京 210016; 2. 北京大学数学科学学院，北京 100871;北京大学数学科学学院，北京 100871 |
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| 基金项目： | 国家自然科学基金(No.10771101). |
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| 摘 要： | 给出了算子值半圆分布的各阶公式.引入算子值随机变量之间一种新的关系-半独立,并在此意义下给出算子值半圆分布的随机矩阵模型.最后证明了若干个半独立的半圆元的矩阵模型是渐进自由的.
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| 关 键 词： | 算子值非交换概率空间 算子值半圆分布 算子值随机矩阵 半独立. |
| 收稿时间： | 2006-10-16 |
| 修稿时间： | 2007-10-28 |
Operator-Valued Semicircular Distribution and Its Asymptotically Free Matrix Models |
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| MENG Bin and GUO Mao Zheng. Operator-Valued Semicircular Distribution and Its Asymptotically Free Matrix Models[J]. Journal of Mathematical Research with Applications, 2008, 28(4): 759-768 |
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| Authors: | MENG Bin and GUO Mao Zheng |
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| Affiliation: | Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Jiangsu 210016, China; School of Mathematical Science, Peking University, Beijing 100871, China;School of Mathematical Science, Peking University, Beijing 100871, China |
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| Abstract: | The moments of operator-valued semicircular distribution are calculated and a new relation between random variables which is called semi-independence is introduced. The asymptotically free matrix models of operator-valued semicircular distribution are given and a method is found to determine the freeness of some semicircular variables. |
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| Keywords: | operator-valued semicircular distribution operator-valued random matrix semi-independence. |
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