论文标题
通过重新归一化的布朗运动，布尔高立方体上的噪声稳定性
Noise stability on the Boolean hypercube via a renormalized Brownian motion
论文作者
论文摘要
我们考虑了布尔超立方体上经典噪声概念的一种变体，该概念引起了有关噪声稳定性不平等的新方法。我们使用这种方法来提供大多数的新证明是Mossel，O'Donnell和Oleszkiewicz的最稳定定理，从而改善了界限对从对数到多项式功能的最大影响的依赖性。我们还表明，法庭和库马尔关于最有用的布尔功能的一种猜想的变体，其中经典噪音被我们的概念取代，这是正确的。我们的方法基于一种随机结构，我们称之为重新归一化的布朗运动，该运动促进了在布尔功能分析时高斯空间中不平等的使用。
We consider a variant of the classical notion of noise on the Boolean hypercube which gives rise to a new approach to inequalities regarding noise stability. We use this approach to give a new proof of the Majority is Stablest theorem by Mossel, O'Donnell, and Oleszkiewicz, improving the dependence of the bound on the maximal influence of the function from logarithmic to polynomial. We also show that a variant of the conjecture by Courtade and Kumar regarding the most informative Boolean function, where the classical noise is replaced by our notion, holds true. Our approach is based on a stochastic construction that we call the renormalized Brownian motion, which facilitates the use of inequalities in Gaussian space in the analysis of Boolean functions.
