On Finite Rank Deformations of Wigner Matrices

Details On Finite Rank Deformations of Wigner Matrices On Finite Rank Deformations of Wigner Matrices

2011-03-18

arxiv.org/abs/1103.3731v4

Mathematics

Probability

accepted for publication in Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistiques

Scientific paper

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrice under the assumption that the off-diagonal matrix entries have uniformly bounded fifth moment and the diagonal entries have uniformly bounded third moment. Using our recent results on the fluctuation of resolvent entries [31],[28], and ideas from [9], we extend results by M.Capitaine, C.Donati-Martin, and D.F\'eral [12], [13].

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