| Issue |
ESAIM: PS
Volume 13, January 2009
|
|
|---|---|---|
| Page(s) | 400 - 408 | |
| DOI | https://doi.org/10.1051/ps:2008018 | |
| Published online | 22 September 2009 | |
Matchings and the variance of Lipschitz functions
1
Institut de Mathématiques de Toulouse,
CNRS UMR 5219, Université Paul Sabatier, 31062 Toulouse Cedex 09, France; barthe@math.univ-toulouse.fr
2
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK.
Received:
24
September
2007
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.
Mathematics Subject Classification: 60D05 / 60F10 / 26D10
Key words: Matching problem / large deviations / variance / spectral gap / Euclidean ball.
© EDP Sciences, SMAI, 2009
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