Fluctuations of the Extreme Eigenvalues of Finite Rank Deformations of Random Matrices

@article{BenaychGeorges2010FluctuationsOT,
  title={Fluctuations of the Extreme Eigenvalues of Finite Rank Deformations of Random Matrices},
  author={Florent Benaych-Georges and Alice Guionnet and Mylene Maida},
  journal={Electronic Journal of Probability},
  year={2010},
  volume={16},
  pages={1621-1662}
}
Consider a deterministic self-adjoint matrix $X_n$ with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limiting measure. We perturb this matrix by adding a random finite rank matrix with delocalised eigenvectors and study the extreme eigenvalues of the deformed model. We give necessary conditions on the deterministic matrix $X_n$ so that the eigenvalues converging out of the bulk exhibit Gaussian… 
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