Non-monotone convergence in the quadratic Wasserstein distance

Details Non-monotone convergence in the quadratic Wasserstein distance Non-monotone convergence in the quadratic Wasserstein distance

2007-04-06

arxiv.org/abs/0704.0876v1

Mathematics

Probability

Scientific paper

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.

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