PIRE - mathematics, mechanics, materials science

Science at the triple point between
mathematics, mechanics and materials science

Publication 85

On the Rate of Convergence of Empirical Measures in ∞ -Transportation Distance

Authors:

CMUNicolás García Trillos
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213


CMUDejan Slepčev
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213


Abstract:
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the of Convergence of Empirical Measures in $\infty$-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
14-CNA-021.pdf

Back to Publications