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A percolation formula. (English) Zbl 1008.60100
Summary: Let \(A\) be an arc on the boundary of the unit disk \(U\). We prove an asymptotic formula for the probability that there is a percolation cluster \(K\) for critical site percolation on the triangular grid in \(U\) which intersects \(A\) and such that \(0\) is surrounded by the union of \(K\) and \(A\).

MSC:
60K35 Interacting random processes; statistical mechanics type models; percolation theory
30C35 General theory of conformal mappings
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