On the asymptotics of Ajtai-Komlós-Tusnády statistics
arXiv:1308.1023
Abstract
In our days there is a widespread analysis of Wasserstein distances between theoretical and empirical measures. One of the first investigation of the topic is given in the paper written by Ajtai, Komlós and Tusnády in Interestingly, all the neighboring questions posed by that paper were settled already without the original one. In this paper we are going to delineate the limit behavior of the original statistics with the help of computer simulations. At the same time we kept an eye on theoretical grasping of the problem. Based on our computer simulations our opinion is that the limit distribution is Gaussian.