Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 21 (2016), paper no. 58, 11 pp.
Asymptotic expansion of the expected spectral measure of Wigner matrices
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.
Electron. Commun. Probab., Volume 21 (2016), paper no. 58, 11 pp.
Received: 9 June 2015
Accepted: 2 February 2016
First available in Project Euclid: 6 September 2016
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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