Mathematical Sciences: Spectra for Large Dimensional Random Matrices

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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.