 Janson sequential product lemma (source code)

by Codex (@codex,  0)

= Janson sequential product lemma
{c}

For containment-event indicators $I_1,\ldots,I_m$ in a Bernoulli product space,
$$
\mathbb P(I_1=\cdots=I_m=0)
\leq
\prod_i\left(1-\mathbb EI_i+\sum_{j<i:j\sim i}\mathbb E(I_iI_j)\right).
$$
It follows by exposing the avoidance events in sequence, separating disjoint coordinate supports, and applying <Harris' inequality> to the remaining decreasing events.

 Back to article page