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.

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.

Keywords

Gaussian noise sensitivity, isoperimetry, influence, Max-Cut

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Date Posted: 27 November 2017

This document has been peer reviewed.