Ronald Meester
Published 2006-08-09Version 1
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.
Comments: Published at http://dx.doi.org/10.1214/074921706000000059 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
Journal: IMS Lecture Notes--Monograph Series 2006, Vol. 48, 37-46
Uniqueness and multiplicity of infinite clusters
$SLE_6$ and 2-d critical bond percolation on the square lattice
A Lemma for Color Switching on the Square Lattice
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