Abstract
Concentration for Limited Independence via Inequalities for the Elementary Symmetric Polynomials
Highlights
The power of independence in probability and randomized algorithms stems from the fact that it lets us control expectations of products of random variables
An important restriction that naturally arises is positivity, where each Xi lies in the interval [0, 1]. This setting of parameters is important for the applications considered in this paper: pseudorandom generators (PRGs) for combinatorial rectangles [7, 12] and minwise independent permutations [4]
Even though we cannot bound E[S (Z)] under k-wise independence once k, we use our new inequalities for symmetric polynomials to get strong tail bounds on them
Summary
The power of independence in probability and randomized algorithms stems from the fact that it lets us control expectations of products of random variables. An important restriction that naturally arises is positivity, where each Xi lies in the interval [0, 1] This setting of parameters (positive variables, small total variance) is important for the applications considered in this paper: pseudorandom generators (PRGs) for combinatorial rectangles [7, 12] and minwise independent permutations [4]. The former is an important problem in the theory of unconditional pseudorandomness which has been studied intensively [7, 12, 19, 3, 13, 9]. We give an overview of the new inequality, its use in the derivation of bounds under limited independence, and the application of these bounds to the construction of pseudorandom generators and hash functions
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