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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Optimal matching and empirical measures


Author: J. E. Yukich
Journal: Proc. Amer. Math. Soc. 107 (1989), 1051-1059
MSC: Primary 60B10; Secondary 60F05, 60F15
MathSciNet review: 1000171
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Abstract: Using results from optimal matching, we find the exact order of convergence for $ \beta ({P_n},P)$ and $ \rho ({P_n},P)$, where $ \beta $ denotes the dual bounded Lipschitz metric, $ \rho $ the Prokhorov metric and $ {P_n}$ the $ n$th empirical measure associated to $ P$, the uniform measure on the unit square. The results solve a long-open problem in empirical measures.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-1000171-8
PII: S 0002-9939(1989)1000171-8
Keywords: Average edge length, minimax matching length, empirical measures, Prokhorov metric, dual bounded Lipschitz metric
Article copyright: © Copyright 1989 American Mathematical Society