Robust Optimality of Gaussian Noise Stability

By Elchanan Mossel, Joe Neeman. 2012

62 citations recorded by the source corpus.

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.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/6ab355d2c364d4649fa8b7a3cc5ef7ea8b839efa

How researchers see this paper

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In Finance

1. Ronen Eldan
2. Joe Neeman
3. Elchanan Mossel

Citations in the corpus

• A two-sided estimate for the Gaussian noise stability deficit (2013, methodology): “ ε(A), with only a logarithmic correction. The lower bound of the estimate we obtain is valid also for the more-general q-stability. As a corollary, we improve the dimension-free robustness result of [MN] which uses the total variation metric, getting the best possible exponent, up to a logarithmic ”
• Robust dimension free isoperimetry in Gaussian space (2012, methodology): “Building on techniques that we develop here, we very recently obtained a robust dimension-free version of Borell’s theorem [23], thereby establishing the applications that we mentioned earlier in the Introduction.”