Matchings and the variance of Lipschitz functions
ESAIM: Probability and Statistics, Tome 13 (2009), pp. 400-408.

We are interested in the rate function of the moderate deviation principle for the two-sample matching problem. This is related to the determination of 1-Lipschitz functions with maximal variance. We give an exact solution for random variables which have normal law, or are uniformly distributed on the euclidean ball.

DOI : 10.1051/ps:2008018
Classification : 60D05, 60F10, 26D10
Mots clés : matching problem, large deviations, variance, spectral gap, euclidean ball 
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Barthe, Franck; O’Connell, Neil. Matchings and the variance of Lipschitz functions. ESAIM: Probability and Statistics, Tome 13 (2009), pp. 400-408. doi : 10.1051/ps:2008018. http://www.numdam.org/articles/10.1051/ps:2008018/

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