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On Finite Rank Deformations of Wigner Matrices

By Alessandro Pizzo, David Renfrew and Alexander Soshnikov

Abstract

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].Comment: accepted for publication in Annales de l'Institut Henri Poincar\'e (B) Probabilit\'es et Statistique

Topics: Mathematics - Probability, 60B20
Year: 2011
OAI identifier: oai:arXiv.org:1103.3731
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