| 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 |
| 算子值半圆分布及其渐进自由矩阵模型 |
| Operator-Valued Semicircular Distribution and Its Asymptotically Free Matrix Models |
| 投稿时间：2006-10-16 修订日期：2007-10-28 |
| DOI：10.3770/j.issn:1000-341X.2008.04.003 |
| 中文关键词: 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. |
| 英文关键词:operator-valued semicircular distribution operator-valued random matrix semi-independence. |
| 基金项目:国家自然科学基金(No.10771101). |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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