Date of this Version
Journal of the European Mathematical Society
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.
Gaussian noise sensitivity, isoperimetry, influence, Max-Cut
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
Date Posted: 27 November 2017
This document has been peer reviewed.