Infinite dimensional isoperimetric inequalities in product spaces with the supremum distance

Journal of Theoretical Probability

Volumn 17, Issue 2, 2004, Pages 293-308

  Barthe, F ^a  

^a CNRS   (France)

Author keywords

Isoperimetric inequalities; Uniform enlargement

Indexed keywords

EID: 4043071953     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOTP.0000020695.25095.c1     Document Type: Article

References (17)

1. Barthe, F. (2001). An isoperimetric result for the Gaussian measure and unconditional sets. Bull. London Math. Soc. 33, 408-416.
2. Barthe, F. (2001). Levels of concentration between exponential and Gaussian. Ann. Fac. Sci. Toulouse 10(3), 393-404.
3. Barthe, F. (2002). Log-concave and spherical models in isoperimetry. Geom. Funct. Anal. 12, 32-55.
4. Barthe, F., and Maurey, B. (2000). Somes remarks on isoperimetry of Gaussian type. Ann. Inst. H. Poincaré Probab. Statist. 36(4), 419-434.
5. Bobkov, S. G. (1996). Extremal properties of half-spaces for log-concave distributions. Ann. Probab. 24(1), 35-48.
6. Bobkov, S. G. (1996). A functional form of the isoperimetric inequality for the Gaussian measure. J. Funct. Anal 135, 39-49.
7. Bobkov, S. G. (1997). An isoperimetric inequality on the discrete cube, and an elementary proof of the isoperimetric inequality in Gauss space. Ann. Probab. 25(1), 206-214.
8. Bobkov, S. G. (1997). Isoperimetric problem for uniform enlargement. Studia Math. 123(1), 81-95.
9. Bobkov, S. G., and Houdré, C. (1996). Characterization of Gaussian measures in terms of the isoperimetric property of half-spaces. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 228, 31-38 (in Russian).
10. Bobkov, S. G., and Houdré, C. (1997). Isoperimetric constants for product probability measures. Ann. Probab. 25(1), 184-205.
11. Bobkov, S. G., and Houdré, C. (2000). Weak dimension-free concentration of measure. Bernoulli 6(4), 621-632.
12. Bobkov, S. G., and Houdré, C. (1997). Some connections between isoperimetric and Sobolev-type inequalities. Mem. Amer. Math. Soc. 129(616), viii+111.
13. Bollobás, B., and Leader, I. (1991). Edge-isoperimetric inequalities in the grid. Combinatorica 11, 299-314.
14. Latała, R., and Oleszkiewicz, K. (2000). Between Sobolev and Poincaré. In Geometric Aspects of Functional Analysis, Lecture Notes in Math., Vol. 1745, Springer, Berlin, pp. 147-168.
15. Ledoux, M. (2001). The Concentration of Measure Phenomenon, Mathematical Surveys and Monographs, Vol. 89, American Mathematical Society, Providence, R.I.
16. Talagrand, M. (1991). A new isoperimetric inequality and the concentration of measure phenomenon. In Lindenstrauss, J., and Milman, V. D. (eds.), Geometric Aspects of Functional Analysis, Lecture Notes in Math., Vol. 1469, Springer-Verlag, Berlin, pp. 94-124.
17. Talagrand, M. (1995). Concentration of measure and isoperimetric inequalities in product spaces. Inst. Hautes Études Sci. Publ. Math. 81, 73-205.