We provide a short proof that the Wasserstein distance between the empirical measure of a n-sample and the estimated measure is of order n^-(1/d), if the measure has a lower and upper bounded density on the d-dimensional flat torus.

翻译：我们简短地证明,如果测量量在二维平面托盘上具有较低和上层边界密度,则正样实测量与估计测量量之间的瓦森斯坦距离是n ⁇ -(1/d)的顺序。