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A percolation formula

Oded Schramm
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Abstract

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 $K\cup A$.

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Oded Schramm. 2001-07-30. A percolation formula. https://arxiv.org/abs/math/0107096

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