# Schramm’s proof of Watts’ formula

```@article{Sheffield2011SchrammsPO,
title={Schramm’s proof of Watts’ formula},
author={Scott Sheffield and David Bruce Wilson},
journal={Annals of Probability},
year={2011},
volume={39},
pages={1844-1863}
}```
• Published 16 March 2010
• Mathematics
• Annals of Probability
G\'{e}rard Watts predicted a formula for the probability in percolation that there is both a left--right and an up--down crossing, which was later proved by Julien Dub\'{e}dat. Here we present a simpler proof due to Oded Schramm, which builds on Cardy's formula in a conceptually appealing way: the triple derivative of Cardy's formula is the sum of two multi-arm densities. The relative sizes of the two terms are computed with Girsanov conditioning. The triple integral of one of the terms is…
18 Citations

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