A Note on Rate of Convergence in Probability to Semicircular Law

2011/05/16 by Bai, Zhidong, Hu, Jiang, Pan, Guangming +1
#FOS: Mathematics #Primary 60F15 #Probability (math.PR) #Secondary 62H99

paper · doi:10.48550/arxiv.1105.3056

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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