I am looking for a reference (not a proof, that I can do) to the following extension of Chernoff.
Let $X_1,..,X_n$ be Boolean random variables, not necessarily independent. Instead, it is guaranteed that $Pr(X_i=1|C)<p$ for each $i$ and every event $C$ that only depends on $\{X_j|j\neq i\}$.
Naturally, I want an upper bound on $\Pr\left(\sum_{i\in[n]}X_i>(1+\lambda)np\right)$.
Thanks in advance!