Greedy is not so bad

Let \Omega be a metric space. There is a natural metric that can be put on the space of all measures on \Omega called the Wasserstein metric. It is obtained by taking the infimum over all couplings of the two measures of the average distance between two points. There is a simple coupling called the...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2002-08, Vol.22 (4), p.1181-1189
Main Author: KALIKOW, STEVEN
Format: Article
Language:English
Online Access:Get full text
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Summary:Let \Omega be a metric space. There is a natural metric that can be put on the space of all measures on \Omega called the Wasserstein metric. It is obtained by taking the infimum over all couplings of the two measures of the average distance between two points. There is a simple coupling called the greedy coupling for the two measures, but operations researchers will assure you that it is terrible to use the value obtained by the greedy coupling as a substitute for the Wasserstein distance between two measures. The purpose of this paper, however, is to show that if all that you are interested in is the topology obtained by the metric, the value you get from the greedy coupling is good enough.
ISSN:0143-3857
1469-4417
DOI:10.1017/S0143385702000718