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arXiv · 0704.0876

Non-monotone convergence in the quadratic Wasserstein distance

Walter Schachermayer·Uwe Schmock·Josef Teichmann
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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.

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Walter Schachermayer, Uwe Schmock, Josef Teichmann. 2007-04-06. Non-monotone convergence in the quadratic Wasserstein distance. https://arxiv.org/abs/0704.0876

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