Exact factorization of correlation functions in 2-D critical percolation

Understand

By use of conformal field theory, we discover several exact factorizations of higher-order density correlation functions in critical two-dimensional percolation.

• Our formulas are valid in the upper half-plane, or any conformally equivalent region.
• We find excellent agreement of our results with high-precision computer simulations.
• There are indications that our formulas hold more generally.