Voronoi Percolation

Voronoi percolation colors the cells of a random Voronoi diagram independently and studies connected paths of one color. In the planar Poisson model at mesh , the nuclei form a homogeneous Poisson point process of intensity , and each cell is black with probability . An annealed probability averages over nuclei and colors, whereas a quenched probability conditions on the nuclei and averages only over colors. For a marked Jordan domain, the crossing convention uses closed black cells intersected with its closure, without additional boundary wiring. Cells whose nuclei lie outside the domain can still participate in a crossing.