Non-monotone convergence in the quadratic Wasserstein distance
Probability
2007-05-23 v1
Abstract
We give an easy counter-example to Problem 7.20 from C. Villani's book on mass transport: in general, the quadratic Wasserstein distance between -fold normalized convolutions of two given measures fails to decrease monotonically.
Keywords
Cite
@article{arxiv.0704.0876,
title = {Non-monotone convergence in the quadratic Wasserstein distance},
author = {Walter Schachermayer and Uwe Schmock and Josef Teichmann},
journal= {arXiv preprint arXiv:0704.0876},
year = {2007}
}