A Note on Rate of Convergence in Probability to Semicircular Law

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

2011-05-16

arxiv.org/abs/1105.3056v1

Mathematics

Probability

13 pages

Scientific paper

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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