Abstract
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.
Information
Published: 1 January 2006
First available in Project Euclid: 28 November 2007
zbMATH: 1125.82006
MathSciNet: MR2306186
Digital Object Identifier: 10.1214/074921706000000059
Subjects:
Primary:
60K35
Secondary:
82B20
Keywords:
cocycle measure
,
cocycles
,
percolation
Rights: Copyright © 2006, Institute of Mathematical Statistics
