Robust optimality of Gaussian noise stability

Mossel, Elchanan, and Neeman, Joe. "Robust optimality of Gaussian noise stability." Journal of the European Mathematical Society 017.2 (2015): 433-482. <http://eudml.org/doc/277260>.

@article{Mossel2015,
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.},
author = {Mossel, Elchanan, Neeman, Joe},
journal = {Journal of the European Mathematical Society},
keywords = {Gaussian noise sensitivity; isoperimetry; influence; Max-Cut; Gaussian noise sensitivity; isoperimetry; influence; max-cut},
language = {eng},
number = {2},
pages = {433-482},
publisher = {European Mathematical Society Publishing House},
title = {Robust optimality of Gaussian noise stability},
url = {http://eudml.org/doc/277260},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Mossel, Elchanan
AU - Neeman, Joe
TI - Robust optimality of Gaussian noise stability
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 2
SP - 433
EP - 482
AB - 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.
LA - eng
KW - Gaussian noise sensitivity; isoperimetry; influence; Max-Cut; Gaussian noise sensitivity; isoperimetry; influence; max-cut
UR - http://eudml.org/doc/277260
ER -