Matchings and the variance of Lipschitz functions

Franck Barthe (1) , Neil O'Connell (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Mathematics Institute

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.

Mots clés: Mathematics

Franck Barthe, Neil O'Connell. Matchings and the variance of Lipschitz functions. ESAIM: Probability and Statistics, 2009, 13, pp.400-408. ⟨10.1051/ps:2008018⟩. ⟨hal-00520009⟩