Uniqueness of percolation on products with Z
Probability
2012-07-31 v2
Abstract
We show that there exists a connected graph G with subexponential volume growth such that critical percolation on the product of G with the line has infinitely many infinite clusters. We also give some conditions under which this cannot occur.
Keywords
Cite
@article{arxiv.1105.2638,
title = {Uniqueness of percolation on products with Z},
author = {Itai Benjamini and Gady Kozma},
journal= {arXiv preprint arXiv:1105.2638},
year = {2012}
}
Comments
10 pages. New version includes one result in the positive direction