Some remarks on isoperimetry of gaussian type

F. Barthe; B. Maurey

Annales de l'I.H.P. Probabilités et statistiques (2000)

  • Volume: 36, Issue: 4, page 419-434
  • ISSN: 0246-0203

How to cite

top

Barthe, F., and Maurey, B.. "Some remarks on isoperimetry of gaussian type." Annales de l'I.H.P. Probabilités et statistiques 36.4 (2000): 419-434. <http://eudml.org/doc/77666>.

@article{Barthe2000,
author = {Barthe, F., Maurey, B.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {isoperimetry; Gaussian measure},
language = {eng},
number = {4},
pages = {419-434},
publisher = {Gauthier-Villars},
title = {Some remarks on isoperimetry of gaussian type},
url = {http://eudml.org/doc/77666},
volume = {36},
year = {2000},
}

TY - JOUR
AU - Barthe, F.
AU - Maurey, B.
TI - Some remarks on isoperimetry of gaussian type
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2000
PB - Gauthier-Villars
VL - 36
IS - 4
SP - 419
EP - 434
LA - eng
KW - isoperimetry; Gaussian measure
UR - http://eudml.org/doc/77666
ER -

References

top
  1. [1] D. Bakry, M. Ledoux, Lévy-Gromov isoperimetric inequality for an infinite dimensional diffusion generator, Invent. Math.123 (1996) 259-281. Zbl0855.58011MR1374200
  2. [2] F. Barthe, Extremal properties of central half-spaces for product measures, Preprint. Zbl0984.28003MR1829243
  3. [3] S.G. Bobkov, A functional form of the isoperimetric inequality for the Gaussian measure, J. Funct. Anal.135 (1996) 39-49. Zbl0838.60013MR1367623
  4. [4] S.G. Bobkov, An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space, Ann. Probab.25 (1997) 206-214. Zbl0883.60031MR1428506
  5. [5] S.G. Bobkov, Isoperimetric and analytic inequalities for log-concave probability measures, to appear in Ann. Probab. Zbl0964.60013MR1742893
  6. [6] S.G. Bobkov, F. Götze, Discrete isoperimetric and Poincaré-type inequalities, Probab. Theory Relat. Fields114 (1999) 245-277. Zbl0940.60028MR1701522
  7. [7] S.G. Bobkov, C. Houdré, Isoperimetric constants for product probability measures, Ann. Probab.25 (1997) 184-205. Zbl0878.60013MR1428505
  8. [8] S.G. Bobkov, M. Ledoux, On modified logarithmic Sobolev inequalities for Bernoulli and Poisson measures, J. Funct. Anal.156 (1998) 347-365. Zbl0920.60002MR1636948
  9. [9] C. Borell, The Brunn-Minkowski inequality in Gauss space, Invent. Math.30 (1975) 207-216. Zbl0292.60004MR399402
  10. [10] M. Capitaine, E.P. Hsu, M. Ledoux, Martingale representation and a simple proof of logarithmic Sobolev inequalities on path spaces, Elect. Comm. in Probab.2 (1997). Zbl0890.60045MR1484557
  11. [11] A. Ehrhard, Symétrisation dans l'espace de Gauss, Math. Scand.53 (1983) 281- 301. Zbl0542.60003MR745081
  12. [12] A. Ehrhard, Inégalités isopérimétriques et intégrales de Dirichlet gaussiennes, Ann. Sci. Ecole Norm. Sup.17 (1984) 317-332. Zbl0546.49020MR760680
  13. [13] H. Federer, Geometric Measure Theory, Grundlehren der mathematischen Wissenschaften153, Springer, Berlin, 1969. Zbl0176.00801MR257325
  14. [14] L. Gross, Logarithmic Sobolev inequalities, Amer. J. Math.97 (1976) 1061-1083. Zbl0318.46049MR420249
  15. [15] H. Hadwiger, Gitterperiodische Punktmengen und Isoperimetrie, Monatsh. Math.76 (1972) 410-418. Zbl0248.52012MR324550
  16. [16] M. Ledoux, The geometry of Markov diffusion generators, at http://www-sv.cict.fr/lsp/Ledoux. Zbl0980.60097
  17. [17] L.C.G. Rogers, D. Williams, Diffusions, Markov Processes and Martingales, Vol. 1: Foundations, 2nd edn., Wiley, 1994. Zbl0826.60002MR1331599
  18. [18] V.N. Sudakov, B.S. Tsirel'son, Extremal propreties of half-spaces for spherically invariant measures, J. Soviet Math.9 (1978) 9-18. Zbl0395.28007
  19. [19] F.Y. Wang, Logarithmic Sobolev inequalities on noncompact Riemannian manifolds, Probab. Theory Related Fields109 (1997) 417-424. Zbl0887.35012MR1481127

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.