Mouvement brownien et inégalité de Hardy dans
Fubini's theorem for double Wiener integrals and the variance of the brownian path
Central limit theorems for eigenvalues of deformations of Wigner matrices
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...
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