Electronic Journal of Probability

A Note on Rate of Convergence in Probability to Semicircular Law

Zhidong Bai, Jiang Hu, Guangming Pan, and Wang Zhou

Full-text: Open access

Abstract

In the present paper, we prove that under the assumption of the finite sixth moment for elements of a Wigner matrix, the convergence rate of its empirical spectral distribution to the Wigner semicircular law in probability is $O(n^{-1/2})$ when the dimension n tends to infinity.

Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 88, 2439-2451.

Dates
Accepted: 23 November 2011
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820257

Digital Object Identifier
doi:10.1214/EJP.v16-963

Mathematical Reviews number (MathSciNet)
MR2861680

Zentralblatt MATH identifier
1244.60022

Subjects
Primary: 60F15: Strong theorems
Secondary: 62H99: None of the above, but in this section

Keywords
convergence rate Wigner matrix Semicircular Law spectral distribution

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Bai, Zhidong; Hu, Jiang; Pan, Guangming; Zhou, Wang. A Note on Rate of Convergence in Probability to Semicircular Law. Electron. J. Probab. 16 (2011), paper no. 88, 2439--2451. doi:10.1214/EJP.v16-963. https://projecteuclid.org/euclid.ejp/1464820257


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References

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