A Note on Rate of Convergence in Probability to Semicircular Law

Published 16 May 2011 in math.PR | (1105.3056v1)

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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