On three-point connectivity in two-dimensional percolation

TL;DR

This paper discusses the universal behavior of three-point connectivity in 2D critical percolation, providing exact results and extending predictions to Potts clusters and subcritical scaling limits.

Contribution

It presents the first exact universal formula for three-point connectivity in 2D critical percolation and offers new predictions for related models and regimes.

Findings

Exact universal result for three-point connectivity

Predictions for Potts clusters

Scaling limit behavior below p_c

Abstract

We argue the exact universal result for the three-point connectivity of critical percolation in two dimensions. Predictions for Potts clusters and for the scaling limit below p_c are also given.