Central limit theorems for eigenvalues of deformations of Wigner matrices

Abstract : In this paper, we study the fluctuations of the extreme eigenvalues of a spiked finite rank deformation of a Hermitian (resp. symmetric) Wigner matrix when these eigenvalues separate from the bulk. We exhibit quite general situations that will give rise to universality or non universality of the fluctuations, according to the delocalization or localization of the eigenvectors of the perturbation. Dealing with the particular case of a spike with multiplicity one, we also establish a necessary and sufficient condition on the associated normalized eigenvector so that the fluctuations of the corresponding eigenvalue of the deformed model are universal.
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2011
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https://hal.archives-ouvertes.fr/hal-00371203
Contributor : Delphine Féral <>
Submitted on : Thursday, September 15, 2011 - 10:53:36 AM
Last modification on : Wednesday, October 11, 2017 - 1:18:52 AM
Document(s) archivé(s) le : Friday, December 16, 2011 - 2:21:27 AM

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  • HAL Id : hal-00371203, version 2
  • ARXIV : 0903.4740

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Mireille Capitaine, Catherine Donati-Martin, Delphine Féral. Central limit theorems for eigenvalues of deformations of Wigner matrices. 2011. 〈hal-00371203v2〉

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