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Publication 14-CNA-021

On the Rate of Convergence of Empirical Measures in $\infty$-Transportation Distance

Nicolas García Trillos
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
ngarciat@andrew.cmu.edu

Dejan Slepčev
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
slepcev@andrew.cmu.edu

Abstract: 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.

Get the paper in its entirety as  14-CNA-021.pdf


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