Percolation crossing probabilities in hexagons: a numerical study

Abstract

In a recent article, one of the authors used $c=0$ logarithmic conformal field theory to predict crossing-probability formulas for percolation clusters inside a hexagon with free boundary conditions. In this article, we verify these predictions with high-precision computer simulations. Our simulations generate percolation-cluster perimeters with hull walks on a triangular lattice inside a hexagon. Each sample comprises two hull walks, and the order in which these walks strike the bottom and upper left/right sides of the hexagon determines the crossing configuration of the percolation sample. We compare our numerical results with the predicted crossing probabilities, finding excellent agreement.

Minor revisions, updated figure 4

References in corpus (3)

• A Guide to Stochastic Loewner Evolution and its Applications
• Percolation Crossing Formulas and Conformal Field Theory
• Numerical results for crossing, spanning and wrapping in two-dimensional percolation