Prahladh Harsha, Adam Klivans, Raghu Meka

Let $X$ be randomly chosen from $\{-1,1\}^n$, and let $Y$ be randomly

chosen from the standard spherical Gaussian on $\R^n$. For any (possibly unbounded) polytope $P$

formed by the intersection of $k$ halfspaces, we prove that

$$\left|\Pr\left[X \in P\right] - \Pr\left[Y \in P\right]\right| \leq \log^{8/5}k ...
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Thomas Vidick

Given two sets $A,B\subseteq\R^n$, a measure of their dependence, or correlation, is given by the expected squared inner product between random $x\in A $ and $y\in B$. We prove an inequality showing that no two sets of large enough Gaussian measure (at least $e^{-\delta n}$ for some constant $\delta >0$) ... more >>>