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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
##### Keywords:
SLE; Cardy; conformal invariance
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