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A note on rate of convergence in probability to semicircular law. (English) Zbl 1244.60022

Summary: 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.

MSC:

60F05 Central limit and other weak theorems
60B20 Random matrices (probabilistic aspects)
62H99 Multivariate analysis