On the Rate of Convergence of Empirical Measures in ∞-transportation Distance. (1st December 2015)

• Record Type: Journal Article
• Authors: García Trillos, Nicolás; Slepčev, Dejan
• Is Part Of: Canadian journal of mathematics. Volume 67:Number 6(2015)
• Page Start: 1358
• Page End: 1383
• Publication Date: 2015-12-01
• Subjects: 60B10 -- 60D05 -- 05C70; optimal transportation -- optimal matching -- infinity transportation distance -- min-max distance -- empirical measure; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2014-044-6
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: 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.