## Institute of Mathematical Statistics Lecture Notes - Monograph Series

- Lecture Notes--Monograph Series
- Volume 48, 2006, 37-46

### A note on percolation in cocycle measures

#### 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.

#### Chapter information

**Source***Dynamics & Stochastics: Festschrift in honor of M. S. Keane* (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006)

**Dates**

First available in Project Euclid: 28 November 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.lnms/1196285806

**Digital Object Identifier**

doi:10.1214/074921706000000059

**Mathematical Reviews number (MathSciNet)**

MR2306186

**Zentralblatt MATH identifier**

1125.82006

**Subjects**

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Secondary: 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs

**Keywords**

percolation cocycles cocycle measure

**Rights**

Copyright © 2006, Institute of Mathematical Statistics

#### Citation

Meester, Ronald. A note on percolation in cocycle measures. Dynamics & Stochastics, 37--46, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2006. doi:10.1214/074921706000000059. https://projecteuclid.org/euclid.lnms/1196285806