Rate of convergence in probability to the Marchenko-Pastur law

Götze F, Tikhomirov A. Rate of convergence in probability to the Marchenko-Pastur law. BERNOULLI. 2004;10(3):503-548.It is shown that the Kolmogorov distance between the spectral distribution function of a random covariance (1/p)XXT, where X is an nxp matrix with independent entries and the distribution function of the Marchenko-Pastur law is of order O(n(-1/2)) in probability. The bound is explicit and requires that the twelfth moment of the entries of the matrix is uniformly bounded and that p/n is separated from 1