Infimum-convolution description of concentration properties of product probability measures, with applications

Paul-Marie Samson

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 3, page 321-338
  • ISSN: 0246-0203

How to cite

top

Samson, Paul-Marie. "Infimum-convolution description of concentration properties of product probability measures, with applications." Annales de l'I.H.P. Probabilités et statistiques 43.3 (2007): 321-338. <http://eudml.org/doc/77936>.

@article{Samson2007,
author = {Samson, Paul-Marie},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {infimum-convolution; concentration; product probability measure; transportation; empirical processes; bin packing problem},
language = {eng},
number = {3},
pages = {321-338},
publisher = {Elsevier},
title = {Infimum-convolution description of concentration properties of product probability measures, with applications},
url = {http://eudml.org/doc/77936},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Samson, Paul-Marie
TI - Infimum-convolution description of concentration properties of product probability measures, with applications
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2007
PB - Elsevier
VL - 43
IS - 3
SP - 321
EP - 338
LA - eng
KW - infimum-convolution; concentration; product probability measure; transportation; empirical processes; bin packing problem
UR - http://eudml.org/doc/77936
ER -

References

top
  1. [1] S. Aida, T. Masuda, I. Shigekawa, Logarithmic Sobolev inequalities and exponential integrability, J. Func. Anal.126 (1994) 83-101. Zbl0846.46020MR1305064
  2. [2] G. Bennett, Probability inequalities for the sum of independent random variables, J. Amer. Statist. Assoc.57 (297) (1962) 33-45. Zbl0104.11905
  3. [3] Bernstein, Sur une modification de l'inégalité de Tchebichef, Annals Science Institute SAV. Ukraine, Sect. Math. I (1924). 
  4. [4] S. Bobkov, F. Gotze, Exponential integrability and transportation cost related to logarithmic Sobolev inequalities, J. Func. Anal.163 (1999) 1-28. Zbl0924.46027MR1682772
  5. [5] S. Bobkov, I. Gentil, M. Ledoux, Hypercontractivity of Hamilton–Jacobi equations, Geom. Funct. Anal.10 (2000) 1028-1052. Zbl1006.47500
  6. [6] S. Boucheron, O. Bousquet, G. Lugosi, P. Massart, Moment inequalities for functions of independent random variables, Ann. Probab.33 (2005) 514-560. Zbl1074.60018MR2123200
  7. [7] S. Boucheron, G. Lugosi, P. Massart, A sharp concentration inequality with applications, Random Structures Algorithms16 (2000) 277-292. Zbl0954.60008MR1749290
  8. [8] S. Boucheron, G. Lugosi, P. Massart, Concentration inequalities using the entropy method, Ann. Probab.31 (2003) 1583-1614. Zbl1051.60020MR1989444
  9. [9] O. Bousquet, A Bennett concentration inequality and its application to suprema of empirical processes, C. R. Acad. Sci. Paris, Ser. I334 (2002) 495-500. Zbl1001.60021MR1890640
  10. [10] O. Bousquet, Concentration inequalities for sub-additive functions using the entropy method, Stochastic Inequalities and Applications56 (2003) 213-247. Zbl1037.60015MR2073435
  11. [11] E.B. Davies, B. Simon, Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians, J. Func. Anal.59 (1984) 335-395. Zbl0568.47034MR766493
  12. [12] G.H. Hardy, J.E. Littlewood, G. Polya, Inequalities, Cambridge Univ. Press, 1964. Zbl0010.10703JFM60.0169.01
  13. [13] T. Klein, Une inegalité de concentration à gauche pour les processus empiriques, C. R. Acad. Sci. Paris, Ser. I334 (2002) 500-505. Zbl1003.60024MR1890641
  14. [14] T. Klein, E. Rio, Concentration around the mean for maxima of empirical processes, Ann. Probab.33 (2005) 1060-1077. Zbl1066.60023MR2135312
  15. [15] M. Ledoux, On Talagrand's deviation inequalities for product measures, ESAIM: Probab. Statist.1 (1996) 63-87. Zbl0869.60013MR1399224
  16. [16] M. Ledoux, The Concentration of Measure Phenomenon, Mathematical Surveys and Monographs, American Mathematical Society, 2001. Zbl0995.60002MR1849347
  17. [17] M. Ledoux, M. Talagrand, Probability in Banach Spaces, Springer-Verlag, Berlin, 1991. Zbl0748.60004MR1102015
  18. [18] G. Lugosi, Concentration-of-measure inequalities, Private communication. 
  19. [19] K. Marton, A measure concentration inequality for contracting Markov chains, Geom. Funct. Anal.6 (1997) 556-571. Zbl0856.60072MR1392329
  20. [20] P. Massart, About the constants in Talagrand's concentration inequalities for empirical processes, Ann. Probab.28 (2000) 863-884. Zbl1140.60310MR1782276
  21. [21] B. Maurey, Some deviation inequalities, Geom. Funct. Anal.1 (1991) 188-197. Zbl0756.60018MR1097258
  22. [22] D. Panchenko, A note on Talagrand's concentration inequalities, Electron. Comm. Probab.6 (2001) 55-65. Zbl0977.60008MR1831801
  23. [23] D. Panchenko, Symmetrization approach to concentration inequalities for empirical processes, Ann. Probab.31 (2003) 2068-2081. Zbl1042.60008MR2016612
  24. [24] W. Rhee, M. Talagrand, A sharp deviation inequality for the stochastic traveling salesman problem, Ann. Probab.17 (1989) 1-8. Zbl0682.68058MR972767
  25. [25] E. Rio, Inégalités de concentration pour les processus empiriques de classes de parties, Probab. Theory Related Fields119 (2000) 163-175. Zbl0976.60033MR1818244
  26. [26] E. Rio, Une inégalité de Bennett pour les maxima de processus empiriques, Ann. Inst. H. Poincaré Probab. Statist.38 (6) (2002) 1053-1058. Zbl1014.60011MR1955352
  27. [27] P.M. Samson, Concentration inequalities for convex functions on Product Spaces, Progr. Probab.56 (2003) 33-52. Zbl1037.60019MR2073425
  28. [28] M. Schmuckenschlager, Private communication. 
  29. [29] M. Talagrand, Concentration of measure and isoperimetric inequalities in product spaces, Publ. Math. Inst. Hautes Études Sci.81 (1995) 73-205. Zbl0864.60013MR1361756
  30. [30] M. Talagrand, New concentration inequalities in product spaces, Invent. Math.126 (1996) 505-563. Zbl0893.60001MR1419006
  31. [31] M. Talagrand, A new look at independence, Ann. Probab.24 (1996) 1-34. Zbl0858.60019MR1387624

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.