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Questions tagged [k-wise-independence]

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5
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1answer
117 views

Analogue of $k$-wise independence for other distributions than uniform

I am looking for the name of the following notion (in order to look it up for myself), and possibly pointers to the corresponding literature. Let $D$ be a fixed distribution over $\{0,1\}^n$, and $1\...
2
votes
1answer
103 views

Optimal bounds for $k$-wise non-uniform random bits

Let $k\geq 2$ be a constant (in my case, $k=4$), and $n,t \geq 0$ be integers such that $2^t \leq n$. What is the smallest sample space (or, equivalent, how many true independent random bits are ...
9
votes
0answers
146 views

Fourth(?) moment method for minimum value

I would like to lower bound the quantity $\Pr[X\ge t, Y\ge t]=\Pr[\min(X,Y)\ge t]$ using the small moments of $X$, $Y$ and $XY$. In particular I am interested in the case where $E[X]=E[Y]=0$, but $E[X ...
3
votes
1answer
110 views

Notion similar to k-wise independence

I want to construct a family of functions $H:\{0,1\}^n \rightarrow \{0,1\}$ with a property that is similar to k-wise independence. Specifically, I want $H$ to satisfy the following property. Let $k$ ...
4
votes
1answer
154 views

How well do subspaces hit sets

Let $S\subset F_2^n$ be a subset of size $\epsilon\cdot 2^n$. Say I choose a random subspace $V$ of dimension $k$ in $F_2^n$. I want to know what is the smallest $k$ such that $V$ `hits' $S$, i.e., $V\...
8
votes
1answer
146 views

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 ...
10
votes
1answer
261 views

Can we construct a k-wise independent permutation on [n] using only constant time and space?

Let $k>0$ be a fixed constant. Given an integer $n$, we want to construct a permutation $\sigma \in S_n$ such that: The construction uses constant time and space (i.e. preprocessing takes ...