Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 14-CNA-021 On the Rate of Convergence of Empirical Measures in $\infty$-Transportation Distance Nicolas García TrillosDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213ngarciat@andrew.cmu.edu Dejan SlepčevDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213slepcev@andrew.cmu.eduAbstract: 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