The Annals of Probability

Extremal properties of half-spaces for log-concave distributions

S. Bobkov

Full-text: Open access

Abstract

The isoperimetric problem for log-concave product measures in $\mathbb{R}^n$ equipped with the uniform distance is considered. Necessary and sufficient conditions under which standard half-spaces are extremal are presented.

Article information

Source
Ann. Probab., Volume 24, Number 1 (1996), 35-48.

Dates
First available in Project Euclid: 15 January 2003

Permanent link to this document
https://projecteuclid.org/euclid.aop/1042644706

Digital Object Identifier
doi:10.1214/aop/1042644706

Mathematical Reviews number (MathSciNet)
MR1387625

Zentralblatt MATH identifier
0859.60048

Subjects
Primary: 60G70: Extreme value theory; extremal processes

Keywords
Isoperimetry

Citation

Bobkov, S. Extremal properties of half-spaces for log-concave distributions. Ann. Probab. 24 (1996), no. 1, 35--48. doi:10.1214/aop/1042644706. https://projecteuclid.org/euclid.aop/1042644706


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References

  • 1 BOBKOV, S. G. 1993. Isoperimetric problem for uniform enlargement. Technical Report 394, Dept. Statistics, Univ. North Carolina.
  • 2 BOBKOV, S. G. 1994. Isoperimetric inequalities for distributions of exponential ty pe. Ann. Probab. 22 978 994.
  • 3 BORELL, C. 1974. Convex measures on locally convex spaces. Ark. Mat. 12 239 252.
  • 4 BORELL, C. 1975. The Brunn Minkowski inequality in Gauss space. Invent. Math. 30 207 216.
  • 5 KURATOWSKI, A. 1966. Topology 1. Academic Press, New York.
  • 6 SUDAKOV, V. N. and TSIREL'SON, B. S. 1978. Extremal properties of half-spaces for spheri cally invariant measures. J. Soviet Math. 9 9 18. Translated from Zap. Nauchn. Z. Z. Sem. Leningrad. Otdel. Mat. Inst. Steklov. 41 1974 14 24 in Russian.
  • 7 TALAGRAND, M. 1991. A new isoperimetric inequality and the concentration of measure Z. phenomenon. Israel Seminar GAFA. Lecture Notes in Math. 1469 94 124. Springer, Berlin.