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 semi-circle 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.
"Asymptotic expansion of the expected spectral measure of Wigner matrices." Electron. Commun. Probab. 21 1 - 11, 2016. https://doi.org/10.1214/16-ECP4351