Geodesic
Robust optimality of Gaussian noise stability
Journal of the European Mathematical Society, Tome 17 (2015) no. 2, pp. 433-482 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/507
Classification : 60-XX, 26-XX, 68-XX
Keywords: Gaussian noise sensitivity, isoperimetry, influence, Max-Cut 
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     author = {Elchanan Mossel and Joe Neeman},
     title = {Robust optimality of {Gaussian} noise stability},
     journal = {Journal of the European Mathematical Society},
     pages = {433--482},
     year = {2015},
     volume = {17},
     number = {2},
     doi = {10.4171/jems/507},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/507/}
}
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Elchanan Mossel; Joe Neeman. Robust optimality of Gaussian noise stability. Journal of the European Mathematical Society, Tome 17 (2015) no. 2, pp. 433-482. doi: 10.4171/jems/507

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