Questions tagged [limited-independence]

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8
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1answer
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A bounded-independence variant of the Berry-Esseen theorem

I came across a presentation by Ryan O'Donnell regarding invariance principles. After proving the Berry-Esseen theorem, there is a slide that discusses extensions of the theorem and one that is ...
8
votes
1answer
266 views

$k$-wise independent probability spaces

I have been having a great deal of difficulty finding a reference that gives simple and straightforward explanation of the following: Suppose we have $n$ random variables $Y_1, \dots, Y_n$, each of $...
4
votes
1answer
94 views

Is being fooled by limited independence preserved by products?

Question. Let $f,g : \{\pm 1\}^n \to \{\pm 1\}$ be $\varepsilon$-fooled by $k$-wise independence -- i.e. for any $k$-wise independent random variable $X$, $\left|\mathbb{E}[f(X)] - \mathbb{E}[f(U)]\...