The Largest Eigenvalue of Rank One Deformation of Large Wigner Matrices |
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| Authors: | Delphine Féral Sandrine Péché |
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| Institution: | (1) Institut de Mathématiques, Laboratoire de Statistique et Probabilités, Université Paul Sabatier, 31062 Toulouse Cedex 9, France;(2) Institut Fourier BP 74, 100 Rue des maths, 38402 Saint Martin d’Heres, France |
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| Abstract: | The purpose of this paper is to establish universality of the fluctuations of the largest eigenvalue for some non-necessarily
Gaussian complex Deformed Wigner Ensembles. The real model is also considered. Our approach is close to the one used by A.
Soshnikov (cf. 11]) in the investigations of classical real or complex Wigner Ensembles. It is based on the computation of
moments of traces of high powers of the random matrices under consideration. |
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