One-Dimensional Empirical Measures, Order Statistics, and Kantorovich Transport Distances

This work is devoted to the study of rates of convergence of the empirical measures $mu_{n} = frac {1}{n} sum_{k=1}^n delta_{X_k}$, $n geq 1$, over a sample $(X_{k})_{k geq 1}$ of independent identically distributed real-valued random variables towards the common distribution $mu$ in Kantorovich transport distances $W_p$.