= Survival and susceptibility thresholds for directed percolation
{title2=$p_H,p_T$}
For the out-cluster $C_x$ in <directed percolation>, define $p_H=\inf\{p:\mathbb P_p(|C_x|=\infty)>0\}$ and $p_T=\inf\{p:\mathbb E_p|C_x|=\infty\}$, with value $1$ when the relevant set is empty below $1$. The first is a survival threshold; the second is a <percolation susceptibility> threshold. Both depend on the root in a general <directed graph>. Exploring a <site percolation> cluster and using each fresh vertex coin for its first tested incoming bond gives a <coupling of probability distributions> with <bond percolation> such that $\theta_s(p)\le p\theta_b(p)$ and $\chi_s(p)\le p\chi_b(p)$. Consequently $p_H^b\le p_H^s$ and $p_T^b\le p_T^s$.
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