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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 |
Appears in Collections: | Staff Publications |
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