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 |