Asymptotic expansion of the expected spectral measure of Wigner matrices

Nathanaël Enriquez (1, 2) , Laurent Ménard (1)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We compute an asymptotic expansion with precision 1/n of the moments of the expected empirical spectral measure of Wigner matrices of size n with independent centered entries. We interpret this expansion as the moments of the addition of the semicircle law and 1/n times an explicit signed measured with null total mass. This signed measure depends only on the second and fourth moments of the entries.

Mots clés: random matrices; moments method

Domaines: Probabilités [math.PR]

Nathanaël Enriquez, Laurent Ménard. Asymptotic expansion of the expected spectral measure of Wigner matrices. 2015. ⟨hal-01162119⟩