Spectra of infinite-dimensional sample covariance matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 2, pp. 309-322
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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.
@article{TMF_2006_148_2_a10,
author = {V. I. Serdobol'skii},
title = {Spectra of infinite-dimensional sample covariance matrices},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {309--322},
publisher = {mathdoc},
volume = {148},
number = {2},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2006_148_2_a10/}
}
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/