t-Wise Independence with Local Dependencies

Ronen Gradwohl, Amir Yehudayoff

Published 2007-06-12Version 1

In this note we prove a large deviation bound on the sum of random variables with the following dependency structure: there is a dependency graph $G$ with a bounded chromatic number, in which each vertex represents a random variable. Variables that are represented by neighboring vertices may be arbitrarily dependent, but collections of variables that form an independent set in $G$ are $t$-wise independent.