The largest eigenvalue of rank one deformation of large Wigner matrices

Details The largest eigenvalue of rank one deformation of large Wigner matrices The largest eigenvalue of rank one deformation of large Wigner matrices

2006-05-23

arxiv.org/abs/math/0605624v1

Mathematics

Probability

Scientific paper

The purpose of this paper is to establish universality of the fluctuations of the largest eigenvalue of 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 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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