Additive/multiplicative free subordination property and limiting   eigenvectors of spiked additive deformations of Wigner matrices and spiked   sample covariance matrices
  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. 
Mireille Capitaine
math.PR