We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport maps and potentials for a large class of costs in R d. We derive a central limit theorem (CLT) towards a Gaussian distribution for the empirical transportation cost under minimal assumptions, with a new proof based on the Efron-Stein inequality and on the sequential compactness of the closed unit ball in L 2 (P) for the weak topology. We provide also CLTs for empirical Wassertsein distances in the special case of potential costs | $\bullet$ | p , p > 1.

翻译：我们考虑了在实证措施与总目标概率之间以一般成本进行最佳运输的问题,用1美元计算。 我们在[19]中推广结果,并证明最佳运输地图和在Rd中可能支付大量费用的可能性都无症状稳定性。 我们得出了一个核心限制理论(CLT),即根据最低假设,用高斯分配实证运输费用,根据Efron-Stein的不平等和L2(P)中较弱的表层封闭单元球的相继紧凑性提出新的证据。我们还为潜在费用的特殊案例提供瓦塞尔特森距离经验的CLT, p > 1。