Absence of site percolation at criticality in Z^2 x {0,1}
Probability
2012-11-20 v1
Abstract
In this note we consider site percolation on a two dimensional sandwich of thickness two, the graph Z^2 x {0,1}. We prove that there is no percolation at the critical point. The same arguments are valid for a sandwich of thickness three with periodic boundary conditions. It remains an open problem to extend this result to other sandwiches.
Keywords
Cite
@article{arxiv.1211.4138,
title = {Absence of site percolation at criticality in Z^2 x {0,1}},
author = {Michael Damron and Charles M. Newman and Vladas Sidoravicius},
journal= {arXiv preprint arXiv:1211.4138},
year = {2012}
}
Comments
13 pages, 3 figures