Geometric influences II: Correlation inequalities and noise sensitivity

Nathan Keller; Elchanan Mossel; Arnab Sen

doi:10.1214/13-AIHP557

Geometric influences II: Correlation inequalities and noise sensitivity

Nathan Keller, Elchanan Mossel, Arnab Sen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 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 language	English
Pages (from-to)	1121-1139
Number of pages	19
Journal	Annales de l'institut Henri Poincare (B) Probability and Statistics
Volume	50
Issue number	4
DOIs	https://doi.org/10.1214/13-AIHP557
State	Published - 1 Nov 2014

Bibliographical note

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

Funding

Funders	Funder number
Division of Computing and Communication Foundations	1320105
Engineering and Physical Sciences Research Council
National Science Foundation	CCF 1320105, DMS 1106999
Office of Naval Research	N00014-14-1-0823
U.S. Department of Defense
National Science Foundation
Directorate for Mathematical and Physical Sciences	1106999
Engineering and Physical Sciences Research Council	EP/G055068/1

Keywords

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

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10.1214/13-AIHP557

Cite this

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Geometric influences II: Correlation inequalities and noise sensitivity

Abstract

Bibliographical note

Funding

Keywords

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