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arXiv · 1105.3056

A Note on Rate of Convergence in Probability to Semicircular Law

Zhidong Bai·Jiang Hu·Guangming Pan·Wang Zhou
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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.

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Zhidong Bai, Jiang Hu, Guangming Pan, Wang Zhou. 2011-05-16. A Note on Rate of Convergence in Probability to Semicircular Law. https://arxiv.org/abs/1105.3056

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