Sprinkling coupling for Bernoulli percolation
= Sprinkling coupling for Bernoulli percolation
For $p<q$, first sample Bernoulli percolation at parameter $p$, then independently open each remaining closed coordinate with probability $(q-p)/(1-p)$. Every coordinate is then open with probability $q$, so the union has the parameter-$q$ law. This coupling separates existing $p$-clusters from the additional sprinkled connections between them.