Non-monotone convergence in the quadratic Wasserstein distance
classification
🧮 math.PR
keywords
distancequadraticwassersteinbookconvergenceconvolutionscounter-exampledecrease
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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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