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Matchings and the variance of Lipschitz functions

Published online by Cambridge University Press:  22 September 2009

Franck Barthe  and
Neil O'Connell
Franck Barthe
Affiliation:
Institut de Mathématiques de Toulouse, CNRS UMR 5219, Université Paul Sabatier, 31062 Toulouse Cedex 09, France; barthe@math.univ-toulouse.fr
Neil O'Connell
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

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-Lipschitzfunctions with maximal variance. We give an exact solution for random variables which havenormal law, or are uniformly distributed on the Euclidean ball.

Keywords

Matching problemlarge deviationsvariancespectral gapEuclidean ball.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 13 , July 2009 , pp. 400 - 408
Copyright
© EDP Sciences, SMAI, 2009

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