t-Wise Independence with Local Dependencies, Information Processing Letters
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.
Ronen Gradwohl, Amir Yehudayoff
Gradwohl, Ronen, and Amir Yehudayoff. 2008. t-Wise Independence with Local Dependencies. Information Processing Letters. 106: 208-212.