Percolation on polygon configurations
Seminar Room 1, Newton Institute
Scullard and Ziff found a simple condition for the self-duality of a family of bond percolation models in the plane, and used it to predict their critical probabilities. This family is wide enough to include models with local dependencies between the states of certain bonds. As in the classical case of bond percolation on the square lattice, the mathematical difficulty is to show that self-duality does imply criticality. Very recently, Oliver Riordan and I proved that this does hold for a family generalizing the models considered by Scullard and Ziff:
in the talk I shall present some of our results concerning this.