A formula for crossing probabilities of critical systems inside polygons

Understand

In this article, we generalize known formulas for crossing probabilities.

• Prior crossing results date back to J.
• Cardy's prediction of a formula for the probability that a percolation cluster in two dimensions connects the left and right sides of a rectangle at the percolation critical point in the continuum limit.
• Here, we predict a new formula for crossing probabilities of a continuum limit loop-gas model on a planar lattice inside a $2N$-sided polygon.