# 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:

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

Dejan 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

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