Electronic Communications in Probability

Asymptotic expansion of the expected spectral measure of Wigner matrices

Nathanaël Enriquez and Laurent Ménard

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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

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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Zentralblatt MATH identifier

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

random matrices moments method

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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

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