## Electronic Journal of Probability

### A Note on Rate of Convergence in Probability to Semicircular Law

#### 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

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

Rights

#### 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

#### References

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