Geodesic
On the Rate of Convergence of Empirical Measures in ∞-transportation Distance
Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1358-1383

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DOI

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.
DOI : 10.4153/CJM-2014-044-6
Mots-clés : 60B10, 60D05, 05C70, optimal transportation, optimal matching, infinity transportation distance, min-maxdistance, empirical measure 
Trillos, Nicolás García; Slepčev, Dejan. On the Rate of Convergence of Empirical Measures in ∞-transportation Distance. Canadian journal of mathematics, Tome 67 (2015) no. 6, pp. 1358-1383. doi: 10.4153/CJM-2014-044-6
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     title = {On the {Rate} of {Convergence} of {Empirical} {Measures} in \ensuremath{\infty}-transportation {Distance}},
     journal = {Canadian journal of mathematics},
     pages = {1358--1383},
     year = {2015},
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