A Note on Rate of Convergence in Probability to Semicircular Law
  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. 
Zhidong Bai, Jiang Hu, Guangming Pan, Wang Zhou
math.PR