A note on percolation in cocycle measures

Details A note on percolation in cocycle measures A note on percolation in cocycle measures

2006-08-09

arxiv.org/abs/math/0608217v1

IMS Lecture Notes--Monograph Series 2006, Vol. 48, 37-46

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921706000000059 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000059

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.

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