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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 absolute 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(On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, Unpublished manuscript; Fluctuations of matrix entries of regular functions of Wigner matrices, Unpublished manuscript) and ideas from (Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Unpublished manuscript), we extend the results by Capitaine, Donati-Martin, and Féral (Ann.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).
Nous étudions la distribution des valeurs propres qui sortent de l'amas du spectre de matrices de Wigner deformées par une matrice de rang fini sous l'hypothèse que les valeurs absolues des éléments non diagonaux aient un moment d'ordre cinq uniformément borné et que valeurs absolues des éléments diagonaux aient un moment d'ordre trois uniformément borné. En utilisant des travaux récents (On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, Unpublished manuscript; Fluctuations of matrix entries of regular functions of Wigner matrices, Unpublished manuscript) et des idées de (Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Unpublished manuscript), nous étendons les résultats de Capitaine, Donati-Martin et Féral (Ann. Probab. 37 (2009) 1-47; Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012) 107-133).
@article{AIHPB_2013__49_1_64_0,
author = {Pizzo, Alessandro and Renfrew, David and Soshnikov, Alexander},
title = {On finite rank deformations of {Wigner} matrices},
journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
pages = {64--94},
publisher = {Gauthier-Villars},
volume = {49},
number = {1},
year = {2013},
doi = {10.1214/11-AIHP459},
mrnumber = {3060148},
zbl = {1278.60014},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1214/11-AIHP459/}
}
TY - JOUR AU - Pizzo, Alessandro AU - Renfrew, David AU - Soshnikov, Alexander TI - On finite rank deformations of Wigner matrices JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2013 SP - 64 EP - 94 VL - 49 IS - 1 PB - Gauthier-Villars UR - http://geodesic.mathdoc.fr/articles/10.1214/11-AIHP459/ DO - 10.1214/11-AIHP459 LA - en ID - AIHPB_2013__49_1_64_0 ER -
%0 Journal Article %A Pizzo, Alessandro %A Renfrew, David %A Soshnikov, Alexander %T On finite rank deformations of Wigner matrices %J Annales de l'I.H.P. Probabilités et statistiques %D 2013 %P 64-94 %V 49 %N 1 %I Gauthier-Villars %U http://geodesic.mathdoc.fr/articles/10.1214/11-AIHP459/ %R 10.1214/11-AIHP459 %G en %F AIHPB_2013__49_1_64_0
Pizzo, Alessandro; Renfrew, David; Soshnikov, Alexander. On finite rank deformations of Wigner matrices. Annales de l'I.H.P. Probabilités et statistiques, Tome 49 (2013) no. 1, pp. 64-94. doi: 10.1214/11-AIHP459
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