= Near-critical percolation power upper bound
{title2=$\theta(p)\leq A(p-1/2)^\beta$}
Suppose a planar <bond percolation> model has critical <one-arm probability> at most $Cn^{-\alpha}$ with $\alpha>0$, and a finite-radius connection event depends on $O(n^2)$ <edges>. The <finite-box comparison for percolation parameters> gives $\theta(p_c+\varepsilon)\leq Cn^{-\alpha}+C'\varepsilon n^2$. Balancing at $n\asymp\varepsilon^{-1/(\alpha+2)}$ gives $\theta(p_c+\varepsilon)\leq A\varepsilon^{\alpha/(\alpha+2)}$. For the <square lattice> use $p_c=1/2$ and the <polynomial critical one-arm upper bound>.
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