Non-monotone convergence in the quadratic Wasserstein distance
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 $n$-fold normalized convolutions of two given measures fails to decrease monotonically.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2007
- DOI:
- 10.48550/arXiv.0704.0876
- arXiv:
- arXiv:0704.0876
- Bibcode:
- 2007arXiv0704.0876S
- Keywords:
-
- Mathematics - Probability;
- 60B10