Mathematical Sciences: Spectra for Large Dimensional Random Matrices

数学科学：大维随机矩阵的谱

• 批准号: 8703090
• 负责人: Yong Yin
• 金额: $ 2.94万
• 依托单位: University of Arizona
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1989-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8703090&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Spectra; Large; Dimensional

The principal investigator intends to study limit distributions of eigenvalues of random matrices of large, asymptotically infinite dimensions. Random matrices are assumed to have i. i. d. columns. Dr. Yin has already obtained certain results on the existence of limit distributions. He now intends to obtain further results in that direction, and to study convergence to the limit distribution when the matrix size goes to infinity, including the case when the ratio of the number of rows to the number of columns tends to zero. The rate of convergence will also be investigated, possibly using some preliminary numerical calculations to get insight into the nature of the problem. Dr. Yin also wants to study the limit value of the maximal and the minimal eigenvalues, where he can employ some combinatorial techniques. Random matrices constitute an active area of research in probability theory. Potential applications of random matrices include signal processing, ecomomic games, computer science and other. Problems studied under this project may be related to studies in signal processing, in particular to those involving a large number of signals and sensors in complex communication systems.

主要研究者打算研究极限分布 渐近无穷大随机矩阵的特征值 尺寸. 假设随机矩阵具有i。I. D.列.博士 尹先生关于极限的存在性已经得到了一定的结果 分布。 他现在打算在这方面取得进一步的成果， 方向，并研究收敛到极限分布时， 矩阵大小趋于无穷大，包括当 行数与列数之比趋于零。 率 收敛也将进行调查，可能使用一些初步的 通过数值计算来深入了解问题的本质。 尹博士还想研究最大值的极限值和 最小特征值，在那里他可以使用一些组合 技术. 随机矩阵构成了一个活跃的研究领域， 概率论。 随机矩阵的潜在应用包括 信号处理，经济游戏，计算机科学和其他。 本项目下研究的问题可能与下列研究有关： 信号处理，特别是涉及大量 复杂通信系统中的信号和传感器。