Matchings and the variance of Lipschitz functions

Franck Barthe; Neil O'Connell

ESAIM: Probability and Statistics (2009)

  • Volume: 13, page 400-408
  • ISSN: 1292-8100

Abstract

top
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.

How to cite

top

Barthe, Franck, and O'Connell, Neil. "Matchings and the variance of Lipschitz functions." ESAIM: Probability and Statistics 13 (2009): 400-408. <http://eudml.org/doc/250654>.

@article{Barthe2009,
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-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. },
author = {Barthe, Franck, O'Connell, Neil},
journal = {ESAIM: Probability and Statistics},
keywords = {Matching problem; large deviations; variance; spectral gap; Euclidean ball.; matching problem; Euclidean ball},
language = {eng},
month = {9},
pages = {400-408},
publisher = {EDP Sciences},
title = {Matchings and the variance of Lipschitz functions},
url = {http://eudml.org/doc/250654},
volume = {13},
year = {2009},
}

TY - JOUR
AU - Barthe, Franck
AU - O'Connell, Neil
TI - Matchings and the variance of Lipschitz functions
JO - ESAIM: Probability and Statistics
DA - 2009/9//
PB - EDP Sciences
VL - 13
SP - 400
EP - 408
AB - 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.
LA - eng
KW - Matching problem; large deviations; variance; spectral gap; Euclidean ball.; matching problem; Euclidean ball
UR - http://eudml.org/doc/250654
ER -

References

top
  1. M. Ajtai, J. Komlós and G. Tusnády, On optimal matchings. Combinatorica 4 (1984) 259–264.  Zbl0562.60012
  2. S.G. Bobkov and F. Götze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities. J. Funct. Anal.163 (1999) 1–28.  Zbl0924.46027
  3. R.M. Dudley, The speed of mean Glivenko-Cantelli convergence. Ann. Math. Stat. 40 (1969) 40–50.  Zbl0184.41401
  4. A. Ganesh and N. O'Connell, Large and moderate deviations for matching problems and empirical discrepancies. Markov Process. Relat. Fields13 (2007) 85–98.  Zbl1156.60019
  5. M. Ledoux, Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi. Ann. Inst. H. Poincaré, Probab. Statist.28 (1992) 267–280.  Zbl0751.60009
  6. M. Ledoux, Concentration of measure and logarithmic Sobolev inequalities, in Séminaire de Probabilités, XXXIII, Lect. Notes Math.1709 120–216. Springer, Berlin (1999).  Zbl0957.60016
  7. C. Müller, Spherical harmonics IV. Springer-Verlag, Berlin-Heidelberg-New York (1966).  Zbl0138.05101
  8. C. Müller and F. Weissler, Hypercontractivity for the heat semigroup for ultraspherical polynomials and on the n-sphere. J. Funct. Anal.48 (1982) 252–283.  Zbl0506.46022
  9. S.T. Rachev, Probability Metrics and the Stability of Stochastic Models. Wiley (1991).  Zbl0744.60004
  10. P.W. Shor, Random planar matching and bin packing , Ph.D. thesis, M.I.T., 1985.  
  11. M. Talagrand, Matching theorems and empirical discrepancy computations using majorizing measures. J. Amer. Math. Soc. 7 (1994) 455–537.  Zbl0810.60036
  12. M. Talagrand, Transportation cost for Gaussian and other product measures. Geom. Funct. Anal.6 (1996) 587–600.  Zbl0859.46030
  13. L. Wu, Large deviations, moderate deviations and LIL for empirical processes. Ann. Probab.22 (1994) 17–27.  Zbl0793.60032

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.