论文标题
球场 - 库马尔最有用的布尔功能猜想和对称的li-médard猜想是同等的
The Courtade-Kumar Most Informative Boolean Function Conjecture and a Symmetrized Li-Médard Conjecture are Equivalent
论文作者
论文摘要
我们认为，朝鲜 - 库马尔最有用的布尔功能对平衡功能的猜想，以及Li andMédard的猜想，即独裁统治功能也最大化了$ l^α$ norm of $ t_pf $ for $ t_pf $ for $ 1 \leqα\leqα\ leq2 $ leq2 $ t_p $，其中$ t_p $是$ f $ f $ f $ f $ f $ f $ a bal tak balance Boolean功能。通过使用1880年代的Laguerre引起的结果，我们能够绑定$ l^α$ - norm相关数量的次数可以作为$α$的函数交叉零，并证明这两个猜想基本上是等效的。
We consider the Courtade-Kumar most informative Boolean function conjecture for balanced functions, as well as a conjecture by Li and Médard that dictatorship functions also maximize the $L^α$ norm of $T_pf$ for $1\leqα\leq2$ where $T_p$ is the noise operator and $f$ is a balanced Boolean function. By using a result due to Laguerre from the 1880's, we are able to bound how many times an $L^α$-norm related quantity can cross zero as a function of $α$, and show that these two conjectures are essentially equivalent.
