A percolation formula

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 $K\cup A$.

7 pages; minor changes from previous version

Cited by in corpus (2)

• Conformal Field Theories of Stochastic Loewner Evolutions
• One-arm exponent for critical 2D percolation