Bounding quantiles of Wasserstein distance between true and empirical measure

Samuel N. Cohen, Martin N. A. Tegnér, Johannes Wiesel

Consider the empirical measure, ${\hat{\mathbb{P}}}_N$, associated to $N$ i.i.d. samples of a given probability distribution $\mathbb{P}$ on the unit interval. For fixed $\mathbb{P}$…