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	A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth
	Li, Yi-Ting ; Liu, Dang-Zheng ; Sun, Xin ; Wang, Zheng-Dong
	2011
关键词	Block Toeplitz matrix GUE GOE Limit spectral distribution
英文摘要	This paper can be thought of as a remark of Li et al. (2010), where the authors studied the eigenvalue distribution mu chi(N) of random block Toeplitz band matrices with given block order m. In this paper, we will give explicit density functions of lim(N ->infinity) mu chi(N), when the bandwidth grows slowly. In fact, these densities are exactly the normalized one-point correlation functions of m x in Gaussian unitary ensemble (CUE for short). The series {lim(N ->infinity) mu chi(N) vertical bar m is an element of N} can be seen as a transition from the standard normal distribution to semicircle distribution. We also show a similar relationship between GOE and block Toeplitz band matrices with symmetric blocks. (C) 2011 Elsevier B.V. All rights reserved.; Statistics & Probability; SCI(E); 0; ARTICLE; 12; 2026-2029; 81
语种	英语
出处	SCI
出版者	statistics probability letters
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/157569]
专题	数学科学学院
推荐引用方式 GB/T 7714	Li, Yi-Ting,Liu, Dang-Zheng,Sun, Xin,et al. A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth. 2011-01-01.

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