Please use this identifier to cite or link to this item: https://doi.org/10.1137/050640424
Title: Semicircle law for Hadamard products
Authors: Bai, Z.D.
Zhang, L.X. 
Keywords: Dilute matrix
Hadamard product
Large dimensional random matrix
Marcẽnko-Pastur law
Random matrix theory
Sample covariance matrix
Semicircle law
Sparse matrix
Spectral distribution
Wigner matrix
Issue Date: 2007
Citation: Bai, Z.D., Zhang, L.X. (2007). Semicircle law for Hadamard products. SIAM Journal on Matrix Analysis and Applications 29 (2) : 473-495. ScholarBank@NUS Repository. https://doi.org/10.1137/050640424
Abstract: In this paper, assuming p/n → 0 as n → ∞, we will prove the weak and strong convergence to the semicircle law of the empirical spectral distribution of the Hadamard product of a normalized sample covariance matrix and a sparsing matrix, which is of the form Ap = 1/√np(X m, nXm, n - σ2nIm) o D m, where the matrices Xm, n and Dm are independent and the entries of Xm, n (m × n) are independent, the matrix Dm (m × m) is Hermitian with independent entries above and on the diagonal, p is the sum of the second moments of the row (and column) entries of Dm, and "o" denotes the Hadamard product of matrices. © 2007 Society for Industrial and Applied Mathematics.
Source Title: SIAM Journal on Matrix Analysis and Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/130445
ISSN: 08954798
DOI: 10.1137/050640424
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