Limit Distributions of Eigenvalues for Random Block Toeplitz and Hankel Matrices

作者：Li Yi Ting; Liu Dang Zheng^*; Wang Zheng Dong

来源：Journal of Theoretical Probability, 2011, 24(4): 1063-1086.

DOI：10.1007/s10959-010-0326-3

• Random block Toeplitz matrix
• Hankel matrix
• Eigenvalues distribution
• Band matrix
• Semicircle law

Block Toeplitz and Hankel matrices arise in many aspects of applications. In this paper, we will research the distributions of eigenvalues for some models and get the semicircle law. Firstly we will give trace formulas of block Toeplitz and Hankel matrix. Then we will prove that the almost sure limit gamma((m))(T) (gamma((m))(H)) of eigenvalue distributions of random block Toeplitz (Hankel) matrices exist and give the moments of the limit distributions where m is the order of the blocks. Then we will prove the existence of almost sure limit of eigenvalue distributions of random block Toeplitz and Hankel band matrices and give the moments of the limit distributions. Finally we will prove that gamma((m))(T) (gamma((m))(H)) converges weakly to the semicircle law as m ->infinity.

• 出版日期2011-12
• 单位北京大学