Central limit theorems for eigenvalues of deformations of Wigner matrices

Mireille Capitaine (1) , Catherine Donati-Martin (2) , Delphine Féral (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 IMB - Institut de Mathématiques de Bordeaux

In this paper, we explain the dependance of the fluctuations of the largest eigenvalues of a Deformed Wigner model with respect to the eigenvectors of the perturbation matrix. We exhibit quite general situations that will give rise to universality or non universality of the fluctuations.

Domaines: Probabilités [math.PR]

Mireille Capitaine, Catherine Donati-Martin, Delphine Féral. Central limit theorems for eigenvalues of deformations of Wigner matrices. 2009. ⟨hal-00371203v1⟩