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Garcia Trillos, Nicolas; Slepcev, Dejan
On the rate of convergence of empirical measures in $\infty$-transportation distance
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is optimal in terms of scaling with the number of sample points.

Keywords:rate, convergence
Category:01B01

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