A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth

Yi-Ting Li, Dang-Zheng Liu, Xin Sun and Zheng-Dong Wang

Statistics & Probability Letters, 2011, vol. 81, issue 12, 2026-2029

Abstract: This paper can be thought of as a remark of Li et al. (2010), where the authors studied the eigenvalue distribution μXN of random block Toeplitz band matrices with given block order m. In this paper, we will give explicit density functions of limN→∞μXN when the bandwidth grows slowly. In fact, these densities are exactly the normalized one-point correlation functions of m×m Gaussian unitary ensemble (GUE for short). The series {limN→∞μXN∣m∈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.

Keywords: Block Toeplitz matrix; GUE; GOE; Limit spectral distribution (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:81:y:2011:i:12:p:2026-2029

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DOI: 10.1016/j.spl.2011.08.016

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