A Tail Bound for Read-k Families of Functions
Gavinsky, Dmytro, Shachar Lovett, Michael Saks, Srikanth Srinivasan · arXiv (Cornell University) · 2012
We prove a Chernoff-like large deviation bound on the sum of non-independent random variables that have the following dependence structure. The variables $Y_1,...,Y_r$ are arbitrary Boolean functions of independent random variables $X_1,...,X_m$, modulo a restriction that every $X_i$ influences at most $k$ of the variables $Y_1,...,Y_r$.