A Tail Bound for Read-k Families of Functions
  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 $Y_1,...,Y_r$. 
Dmytro Gavinsky, Shachar Lovett, Michael Saks, Srikanth Srinivasan
cs.DM math.PR