Tight Chernoff-Like Bounds Under Limited Independence

TL;DR

This paper derives precise bounds on the moments of sums of k-wise independent bounded variables with limited variance, improving previous results and offering applications like sharp binomial moment bounds.

Contribution

It introduces new tight bounds on moments of k-wise independent variables under variance constraints, advancing the understanding of their probabilistic behavior.

Findings

Established sharp bounds on moments of k-wise independent variables.

Extended results to asymptotically sharp binomial moment bounds.

Closed gaps in previous research by Schmidt et al. and Bellare, Rompel.

Abstract

This paper develops sharp bounds on moments of sums of k-wise independent bounded random variables, under constrained average variance. The result closes the problem addressed in part in the previous works of Schmidt et al. and Bellare, Rompel. We The work also discuss discusses other applications of independent interests, such as asymptotically sharp bounds on binomial moments.