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- W4300288034 abstract "Consider the random matrix $Sigma = D^{1/2} X widetilde D^{1/2}$ where $D$ and $widetilde D$ are deterministic Hermitian nonnegative matrices with respective dimensions $N times N$ and $n times n$, and where $X$ is a random matrix with independent and identically distributed centered elements with variance $1/n$. Assume that the dimensions $N$ and $n$ grow to infinity at the same pace, and that the spectral measures of $D$ and $widetilde D$ converge as $N,n toinfty$ towards two probability measures. Then it is known that the spectral measure of $SigmaSigma^*$ converges towards a probability measure $mu$ characterized by its Stieltjes Transform. In this paper, it is shown that $mu$ has a density away from zero, this density is analytical wherever it is positive, and it behaves in most cases as $sqrt{|x - a|}$ near an edge $a$ of its support. A complete characterization of the support of $mu$ is also provided. Beside its mathematical interest, this analysis finds applications in a certain class of statistical estimation problems." @default.
- W4300288034 created "2022-10-03" @default.
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- W4300288034 date "2013-10-30" @default.
- W4300288034 modified "2023-09-26" @default.
- W4300288034 title "Analysis of the limiting spectral measure of large random matrices of the separable covariance type" @default.
- W4300288034 hasPublicationYear "2013" @default.
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