A note on percolation in cocycle measures [chapter]

Ronald Meester
2006 Institute of Mathematical Statistics Lecture Notes - Monograph Series  
We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a very specific form and direction. In concrete situations, this leads to a quick decision whether or not a certain cocycle measure percolates. We illustrate this with two examples which are interesting in their own right.
doi:10.1214/074921706000000059 fatcat:xuhng5nuzre75gxtsghzz5rg6m