Exact factorization of correlation functions in 2-D critical percolation

TL;DR

This paper derives exact formulas for higher-order correlation functions in 2D critical percolation using conformal field theory, validated by simulations and potentially applicable more broadly.

Contribution

It provides the first exact factorization formulas for higher-order correlation functions in 2D critical percolation, extending the understanding of conformal invariance.

Findings

Exact correlation function factorizations derived

High-precision simulations confirm theoretical predictions

Formulas likely applicable to broader conformal regions

Abstract

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.