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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/8756

Title: A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth
Authors: Li, Y.T.
Liu, D.Z.
Sun, X.
Wang, Z.D.
Keywords: Block Toeplitz matrix
Limit spectral distribution
Issue Date: Dec-2011
Citation: STATISTICS & PROBABILITY LETTERS Volume: 81 Issue: 12 Pages: 2026-2029 DOI: 10.1016/j.spl.2011.08.016
Abstract: 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.
Description: Liu, DZ (Liu, Dang-Zheng). Univ Talca, Inst Matemat & Fis, Talca, Chile
URI: http://dspace.utalca.cl/handle/1950/8756
ISSN: 0167-7152
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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