Electronic Communications in Probability

Asymptotic expansion of the expected spectral measure of Wigner matrices

Nathanaël Enriquez and Laurent Ménard

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1473186615

Digital Object Identifier
doi:10.1214/16-ECP4351

Zentralblatt MATH identifier
1348.60009

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Keywords
random matrices moments method

Rights
Creative Commons Attribution 4.0 International License.

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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References

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