论文标题
等级不平等变得更简单
Isoperimetric Inequalities Made Simpler
论文作者
论文摘要
我们提供了一种替代，简单的方法，以证明超立方体上的等等数量不平等。特别是，我们表明： 1。塔拉格兰（Talagrand）的经典等速度不平等的基本证据，以及塔拉格兰（Talagrand）的更强的等轴测结果，最近由埃尔丹（Eldan）和格罗斯（Eldan）和格罗斯（Eldan）和格罗斯（Gross）证明。 2。加强Friedgut Junta定理，断言，如果$ p $ - 函数灵敏度的敏感性对于约1/2 + \ VAREPSILON \ LEQ P \ leq 1 $是恒定的，那么该功能就接近Junta。用这种语言，弗里德古特的定理是$ p = 1 $的特殊情况。
We give an alternative, simple method to prove isoperimetric inequalities over the hypercube. In particular, we show: 1. An elementary proof of classical isoperimetric inequalities of Talagrand, as well as a stronger isoperimetric result conjectured by Talagrand and recently proved by Eldan and Gross. 2. A strengthening of the Friedgut junta theorem, asserting that if the $p$-moment of the sensitivity of a function is constant for some $1/2 + \varepsilon\leq p\leq 1$, then the function is close to a junta. In this language, Friedgut's theorem is the special case that $p=1$.
