A percolation formula

Details A percolation formula A percolation formula

2001-07-13

arxiv.org/abs/math/0107096v2

Electron. Comm. Probab. vol. 6, paper no. 12, 115--120, 2001; http://www.math.washington.edu/~ejpecp/EcpVol6/paper12.abs.html

Mathematics

Probability

7 pages; minor changes from previous version

Scientific paper

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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