The extreme eigenvalues of two types of random matrices

Abstract

The fluctuations of extreme eigenvalues of a large random matrix model is a central topic in random matrix theory, motivated by applications in principle component analysis, factor analysis, or signal detection problems. This thesis establishes asymptotic distributions for the largest eigenvalues of two types of matrices under the high dimensional setting where the dimension goes to infinity proportionally with the sample size.I would like to express my deep and sincere attitude to my supervisor, Professor Pan Guangming, for his invaluable guidance and unfailing encouragement throughout my Ph.D. study. He led me to the scientific research, raised many interesting questions to me, and helped me a lot with his wide knowledge. I feel very fortunate for having the opportunity to work with him. I would like to thank Division of Mathematical Sciences of Nanyang Technological university for providing me the scholarships for pursuing the research study. I am thankful to my thesis committee members, Prof. Xiang Liming and Prof. Feng Qu for their help and guidance. I also appreciate many teachers, Prof.