Percolation in Voronoi tilings


We consider a percolation process on a random tiling of ℝ into Voronoi cells based on points of a realization of a Poisson process. We prove the existence of a phase transition as the proportion p of open cells is varied and provide estimates for the critical probability p c. Specifically, we prove that for large d, 2 -d(9d log d) -1 ≤ P c(d) ≤ C2 -d √d log d. © 2004 Wiley Periodicals, Inc.

Publication Title

Random Structures and Algorithms