弹性函数噪声相关的高斯界
Gaussian Bounds for Noise Correlation of Resilient Functions
摘要：
函数噪声相关性的高斯界在逼近的困难性、定量社会选择理论和检验中起着重要的作用。作者（2008）获得了$\ell$低影响函数$f^{(1)},\ldots, f^{(\ell)} : Ω^n \to [0,1]$的预期相关性的尖锐高斯界，其中函数的输入通过$Ω^{\ell}$上的$n$ -倍分布张量$\mathcal{P}$相关。很自然地会问，低影响的条件是否可以放宽到函数的傅里叶系数为零的条件。在这里，我们肯定地回答这个问题。对于两个功能$f$和$g$的情况下，我们进一步表明，如果$f,g$有一个嘈杂的内积，超过高斯界，那么他们的大系数相交的傅立叶支持。
英文摘要：
Gaussian bounds on noise correlation of functions play an important role in hardness of approximation, in quantitative social choice theory and in testing. The author (2008) obtained sharp gaussian bounds for the expected correlation of $\ell$ low influence functions $f^{(1)},\ldots, f^{(\ell)} : Ω^n \to [0,1]$, where the inputs to the functions are correlated via the $n$-fold tensor of distribution $\mathcal{P}$ on $Ω^{\ell}$. It is natural to ask if the condition of low influences can be relaxed to the condition that the function has vanishing Fourier coefficients. Here we answer this question affirmatively. For the case of two functions $f$ and $g$, we further show that if $f,g$ have a noisy inner product that exceeds the gaussian bound, then the Fourier supports of their large coefficients intersect.
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