Additive/multiplicative free subordination property and limiting eigenvectors of spiked additive deformations of Wigner matrices and spiked sample covariance matrices

Details Additive/multiplicative free subordination property and limiting eigenvectors of spiked additive deformations of Wigner matrices and spiked sample covariance matrices Additive/multiplicative free subordination property and limiting eigenvectors of spiked additive deformations of Wigner matrices and spiked sample covariance matrices

2011-03-15

arxiv.org/abs/1103.2899v3

Mathematics

Probability

Scientific paper

When some eigenvalues of a spiked multiplicative resp. additive deformation model of a Hermitian Wigner matrix resp. a sample covariance matrix separate from the bulk, we study how the corresponding eigenvectors project onto those of the perturbation. We point out that the inverse of the subordination function relative to the free additive resp. multiplicative convolution plays an important part in the asymptotic behavior.

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