Open Access
VOL. 48 | 2006 A note on percolation in cocycle measures
Ronald Meester

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy

IMS Lecture Notes Monogr. Ser., 2006: 37-46 (2006) DOI: 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.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1125.82006
MathSciNet: MR2306186

Digital Object Identifier: 10.1214/074921706000000059

Primary: 60K35
Secondary: 82B20

Keywords: cocycle measure , cocycles , percolation

Rights: Copyright © 2006, Institute of Mathematical Statistics

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