Statistics Papers
Document Type
Journal Article
Date of this Version
2015
Publication Source
Journal of the European Mathematical Society
Volume
17
Issue
2
Start Page
433
Last Page
482
DOI
10.4171/JEMS/507
Abstract
We prove that under the Gaussian measure, half-spaces are uniquely the most noise stable sets. We also prove a quantitative version of uniqueness, showing that a set which is almost optimally noise stable must be close to a half-space. This extends a theorem of Borell, who proved the same result but without uniqueness, and it also answers a question of Ledoux, who asked whether it was possible to prove Borell’s theorem using a direct semigroup argument. Our quantitative uniqueness result has various applications in diverse fields.
Keywords
Gaussian noise sensitivity, isoperimetry, influence, Max-Cut
Recommended Citation
Mossel, E., & Neeman, J. (2015). Robust Optimality of Gaussian Noise Stability. Journal of the European Mathematical Society, 17 (2), 433-482. http://dx.doi.org/10.4171/JEMS/507
Included in
Mathematics Commons, Other Physical Sciences and Mathematics Commons, Statistics and Probability Commons
Date Posted: 27 November 2017
This document has been peer reviewed.
Comments
At the time of publication, author Elchanan Mossel was affiliated with the University of California, Berkeley. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.