Open Access
2016 Asymptotic expansion of the expected spectral measure of Wigner matrices
Nathanaël Enriquez, Laurent Ménard
Electron. Commun. Probab. 21: 1-11 (2016). DOI: 10.1214/16-ECP4351


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.


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Nathanaël Enriquez. Laurent Ménard. "Asymptotic expansion of the expected spectral measure of Wigner matrices." Electron. Commun. Probab. 21 1 - 11, 2016.


Received: 9 June 2015; Accepted: 2 February 2016; Published: 2016
First available in Project Euclid: 6 September 2016

zbMATH: 1348.60009
MathSciNet: MR3548770
Digital Object Identifier: 10.1214/16-ECP4351

Primary: 60B20

Keywords: Moments method , random matrices

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