Electronic Communications in Probability

A Percolation Formula

Oded Schramm

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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 $A$.

Article information

Electron. Commun. Probab., Volume 6 (2001), paper no. 12, 115-120.

Accepted: 24 October 2001
First available in Project Euclid: 19 April 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 30C35: General theory of conformal mappings

SLE Cardy conformal invariance

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Schramm, Oded. A Percolation Formula. Electron. Commun. Probab. 6 (2001), paper no. 12, 115--120. doi:10.1214/ECP.v6-1041. https://projecteuclid.org/euclid.ecp/1461097557

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