= Random-cluster single-edge conditional probability
{title2=$\phi(\omega(e)=1\mid\omega_{E\setminus e})\in\{p,\ p/(p+q(1-p))\}$}
For an edge with endpoints already connected without that edge, including any boundary wiring, the conditional open <probability> is $p$. Otherwise opening the edge merges two components, so the <conditional probability> is $p/(p+q(1-p))$. For $q\geq1$, this <conditional probability> increases when more other edges are open or more boundary vertices are identified. This is the local mechanism of <boundary monotonicity of the random-cluster measure>.
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