= Boundary-side amplification for planar percolation
{title2=$P(E_T\cap E_B)\ge1-2(1-P(D_N))^{1/4}$}
If an <infinite percolation cluster> exists almost surely, the <probability> that a large square box intersects one tends to one. The four rotationally symmetric exterior-side arm events are increasing. By the <Harris-FKG inequality>, their common <probability> is at least $1-(1-P(D_N))^{1/4}$, where $D_N$ is their union. Thus a pair of specified opposite sides both has an infinite exterior arm with <probability> at least $1-2(1-P(D_N))^{1/4}$, tending to one. The rays start at a boundary <graph vertex> and immediately leave the <graph vertex> box.
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