## Electronic Communications in Probability

### Asymptotic expansion of the expected spectral measure of Wigner matrices

#### Abstract

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.

#### Article information

Source
Electron. Commun. Probab. Volume 21 (2016), paper no. 58, 11 pp.

Dates
Accepted: 2 February 2016
First available in Project Euclid: 6 September 2016

https://projecteuclid.org/euclid.ecp/1473186615

Digital Object Identifier
doi:10.1214/16-ECP4351

Zentralblatt MATH identifier
1348.60009

Keywords
random matrices moments method

#### Citation

Enriquez, Nathanaël; Ménard, Laurent. Asymptotic expansion of the expected spectral measure of Wigner matrices. Electron. Commun. Probab. 21 (2016), paper no. 58, 11 pp. doi:10.1214/16-ECP4351. https://projecteuclid.org/euclid.ecp/1473186615

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