Mathematical Sciences: Spectra for Large Dimensional Random Matrices

主要研究者打算研究大的，渐近无限维的随机矩阵的特征值的极限分布。假设随机矩阵有i. i. d列。Yin博士已经对极限分布的存在性得到了一定的结果。他现在打算在这个方向上得到进一步的结果，并研究当矩阵的大小趋于无穷时收敛到极限分布，包括当行数与列数之比趋于零的情况。还将研究收敛速度，可能会使用一些初步的数值计算来深入了解问题的本质。尹博士还想研究最大和最小特征值的极限值，在那里他可以使用一些组合技术。随机矩阵是概率论中一个活跃的研究领域。随机矩阵的潜在应用包括信号处理、经济博弈、计算机科学等。本项目研究的问题可能与信号处理研究有关，特别是涉及复杂通信系统中大量信号和传感器的研究。

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.