= Random-cluster weight monotonicity
{title2=$q_1\le q_2\Longrightarrow\mu_{p,q_1}\succeq\mu_{p,q_2}$}
For fixed $p\in(0,1)$ and $1\le q_1\le q_2$, the <random-cluster measure> at $q_1$ <stochastically dominates> that at $q_2$. In <Holley's condition>, Bernoulli factors cancel. Put $a=k(S)-k(S\cup T)$ and $b=k(S\cap T)-k(T)$; <supermodularity of graph component count> gives $b\ge a\ge0$, and the weight ratio is $(q_2/q_1)^a q_2^{b-a}\ge1$. The comparison also holds with the same boundary wiring in both measures.
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