= Percolation triangle condition
{title2=$\sum_{x,y}\tau(0,x)\tau(x,y)\tau(y,0)<\infty$}
Here $\tau(x,y)=P_{p_c}(x\leftrightarrow y)$ is critical two-point connectivity. The condition controls the intersection effects that spoil a branching approximation. It is a sufficient criterion for important <mean-field percolation exponents>, including the order-parameter, <percolation susceptibility> and cluster-tail exponents. Establishing detailed spatial asymptotics is a further task, commonly addressed by <lace expansion>.
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