On the rate of convergence of empirical measures in $\infty$-transportation distance

Nicolás García Trillos, Dejan Slepčev

Published 2014-07-04Version 1

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.