Institute of Mathematical Statistics Lecture Notes - Monograph Series

A note on percolation in cocycle measures

Ronald Meester

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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
Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy, eds., Dynamics & Stochastics: Festschrift in honor of M. S. Keane (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2006), 37-46

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


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