Limiting spectral distribution of block matrices with Toeplitz block structure

Riddhipratim Basu, Arup Bose, Shirshendu Ganguly and Rajat Subhra Hazra

Statistics & Probability Letters, 2012, vol. 82, issue 7, 1430-1438

Abstract: We study two specific symmetric random block Toeplitz (of dimension k×k) matrices, where the blocks (of size n×n) are (i) matrices with i.i.d. entries and (ii) asymmetric Toeplitz matrices. Under suitable assumptions on the entries, their limiting spectral distributions (LSDs) exist (after scaling by nk) when (a) k is fixed and n→∞ (b) n is fixed and k→∞ (c) n and k go to ∞ simultaneously. Further, the LSDs obtained in (a) and (b) coincide with those in (c) when n or respectively k tends to infinity. This limit in (c) is the semicircle law in Case (i). In Case (ii), the limit is related to the limit of the random symmetric Toeplitz matrix as obtained by Bryc et al. (2006) and Hammond and Miller (2005).

Keywords: Block random matrices; Limiting spectral distribution; Toeplitz matrix; Wigner matrix (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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DOI: 10.1016/j.spl.2012.04.004

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