Geodesic
Spectra of infinite-dimensional sample covariance matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 309-322 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study spectral functions of infinite-dimensional random Gram matrices of the form $RR^{\mathrm{T}}$, where $R$ is a rectangular matrix with an infinite number of rows and with the number of columns $N\to\infty$, and the spectral functions of infinite sample covariance matrices calculated for samples of volume $N\to\infty$ under conditions analogous to the Kolmogorov asymptotic conditions. We assume that the traces $d$ of the expectations of these matrices increase with the number $N$ such that the ratio $d/N$ tends to a constant. We find the limiting nonlinear equations relating the spectral functions of random and nonrandom matrices and establish the asymptotic expression for the resolvent of random matrices.
Keywords: spectra of random matrices, spectral functions of sample covariance matrices, spectra of infinite-dimensional random matrices. 
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V. I. Serdobol'skii. Spectra of infinite-dimensional sample covariance matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 309-322. http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a10/

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