Robust Optimality of Gaussian Noise Stability
Robust Optimality of Gaussian Noise Stability
复制标题
高斯噪声稳定性的鲁棒最优性
DOI：
10.4171/jems/507
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Joe Neeman
中科院分区：
文献类型：
--
作者：
Elchanan Mossel;Joe Neeman
证明了在高斯测度下，半空间是唯一的最噪声稳定集。我们还证明了一个定量版本的唯一性，表明一组几乎是最佳噪声稳定必须接近半空间。这扩展了一个定理的博雷尔，谁证明了同样的结果，但没有唯一性，它也回答了一个问题的勒杜，谁问是否有可能证明博雷尔的定理使用直接半群的论点。我们的定量唯一性结果在不同的领域有不同的应用。
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.