Geometric influences II: Correlation inequalities and noise sensitivity

Nathan Keller, Elchanan Mossel, Arnab Sen

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

In a recent paper, we presented a new definition of influences in product spaces of continuous distributions, and showed that analogues of the most fundamental results on discrete influences, such as the KKL theorem, hold for the new definition in Gaussian space. In this paper we prove Gaussian analogues of two of the central applications of influences: Talagrand's lower bound on the correlation of increasing subsets of the discrete cube, and the Benjamini-Kalai-Schramm (BKS) noise sensitivity theorem. We then use the Gaussian results to obtain analogues of Talagrand's bound for all discrete probability spaces and to reestablish analogues of the BKS theorem for biased two-point product spaces.

Original languageEnglish (US)
Pages (from-to)1121-1139
Number of pages19
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Volume50
Issue number4
DOIs
StatePublished - Nov 1 2014

Bibliographical note

Publisher Copyright:
© Association des Publications de l'Institut Henri Poincaré, 2014

Keywords

  • Correlation between increasing sets
  • Gaussian measure
  • Geometric influences
  • Influences
  • Isoperimetric inequality
  • Noise sensitivity
  • Talagrand's bound

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