Discrete isoperimetric and Poincaré-type inequalities

S. G. Bobkov, F. Götze

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

We study some discrete isoperimetric and Poincaré-type inequalities for product probability measures μn on the discrete cube {0, 1}n and on the lattice Zn. In particular we prove sharp lower estimates for the product measures of 'boundaries' of arbitrary sets in the discrete cube. More generally, we characterize those probability distributions μ on Z which satisfy these inequalities on Zn. The class of these distributions can be described by a certain class of monotone transforms of the two-sided exponential measure. A similar characterization of distributions on R which satisfy Poincaré inequalities on the class of convex functions is proved in terms of variances of suprema of linear processes.

Original languageEnglish (US)
Pages (from-to)245-277
Number of pages33
JournalProbability Theory and Related Fields
Volume114
Issue number2
DOIs
StatePublished - Jun 1999
Externally publishedYes

Keywords

  • Concentration of measure
  • Isoperimetry
  • Poincaré inequalities

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