= Root-moment bound for open self-avoiding walks
{title2=$\mathbb E(\kappa_n^{1/n})\leq p c_n^{1/n}$}
In independent <bond percolation> on a <graph>, let $c_n$ be the number of $n$-step <self-avoiding walks> from a fixed <graph vertex> and $\kappa_n$ the number that are open. Then $\mathbb E\kappa_n=c_np^n$. The <Jensen inequality> for the <concave function> $t^{1/n}$ gives $\mathbb E(\kappa_n^{1/n})\leq p c_n^{1/n}$. No <independence> between different <self-avoiding walk> indicators is needed. When $c_n^{1/n}\to\mu$, the <limit superior> is at most $p\mu$.
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