Connective-constant lower bound for percolation
= Connective-constant lower bound for percolation
{title2=$p_c\geq\mu^{-1}$}
For independent <bond percolation> on a transitive locally finite lattice, let $c_n$ count rooted <self-avoiding walks> and let $\mu=\lim c_n^{1/n}$ be the <connective constant>. An infinite open <percolation cluster> supplies an open walk of every length. The <union bound> gives $\theta(p)\leq c_np^n$, which tends to zero when $p\mu<1$. Thus $p_c\geq1/\mu$.