Matchings and the variance of Lipschitz functions

Barthe, Franck; O’Connell, Neil

doi:10.1051/ps:2008018

Cited by 3 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A numerical investigation of the distribution of the statistic was given in [8]. Matchings on the Euclidean ball were investigated in [3]. The paper [13] investigates the rate of convergence in abstract settings.…”

Section: Historymentioning

confidence: 99%

On the asymptotics of Ajtai-Komlós-Tusnády statistics

Rejtő¹,

Tusnády²

2013

Preprint

View full text Add to dashboard Cite

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 1984. 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.

show abstract

Section: Historymentioning

confidence: 99%

On the asymptotics of Ajtai-Komlós-Tusnády statistics

Rejtő¹,

Tusnády²

2013

Preprint

View full text Add to dashboard Cite

show abstract

“…In particular, their main result consist in a MDP over the unit square as well as a LDP over a compact metric space, where the rate function is characterized as a solution to a variational problem. Later Barthe and O'Connell [2009] extended this result to compact support in R d , and they obtained that the exact moderate deviation rate function on the unit hypercube, is equal to (d+2) 4 x 2 . Their proof is essentially the same, combining large and moderate deviation results for empirical measures given in Wu [1994] (which relies heavily on earlier work of Ledoux [1992]) with convergence rates for empirical measures in the Monge-Kantorovich distance due to Dudley [1969] and for the unbounded case to Rachev [1991].…”

Section: Introductionmentioning

confidence: 94%