We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices under the assumption that the absolute values of the off-diagonal matrix entries have uniformly bounded fifth moment and the abso- lute values of the diagonal entries have uniformly bounded third moment. Using our recent results on the fluctuation of resolvent entries (On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, Unpub- lished manuscript; Fluctuations of matrix entries of regular functions of Wigner matrices, Unpublished manuscript) and ideas from (Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Unpublished manuscript), we extend the results by Capitaine, Donati-Martin, and Féral (Ann. Probab. 37 (2009) 1–47; Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012) 107–133).

Pizzo, A., Renfrew, D., & Soshnikov, A. (2013). On finite rank deformations of Wigner matrices. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 49(1), 64-94 [10.1214/11-AIHP459].

On finite rank deformations of Wigner matrices

PIZZO, ALESSANDRO;
2013

Abstract

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices under the assumption that the absolute values of the off-diagonal matrix entries have uniformly bounded fifth moment and the abso- lute values of the diagonal entries have uniformly bounded third moment. Using our recent results on the fluctuation of resolvent entries (On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, Unpub- lished manuscript; Fluctuations of matrix entries of regular functions of Wigner matrices, Unpublished manuscript) and ideas from (Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Unpublished manuscript), we extend the results by Capitaine, Donati-Martin, and Féral (Ann. Probab. 37 (2009) 1–47; Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012) 107–133).
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/07 - Fisica Matematica
English
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Pizzo, A., Renfrew, D., & Soshnikov, A. (2013). On finite rank deformations of Wigner matrices. ANNALES DE L'INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 49(1), 64-94 [10.1214/11-AIHP459].
Pizzo, A; Renfrew, D; Soshnikov, A
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2108/134577
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