= Percolation one-arm decay rate
{title2=$\gamma(p)=\lim g_n^{1/n}$}
For <bond percolation> on the <square lattice>, the <one-arm probability> $g_n=\mathbb P_p(0\leftrightarrow\partial[-n,n]^2)$ has a root <limit of a sequence> $\gamma(p)\in[p,1]$. The <BK boundary-splitting estimate> implies that $32n^2g_n$ is submultiplicative for positive integers. Applying the <Fekete lemma> to its logarithm proves existence when $p>0$; at $p=0$ the rate is zero. The same rate is the root limit of the <percolation two-point connection probability> along a coordinate axis, by the <reflection lower bound for two-point percolation>.
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