### 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.

Original language | Undefined |
---|---|

Article number | 1211.4138 |

Journal | arXiv |

State | Published - Nov 17 2012 |

### Keywords

- math.PR

## Cite this

Damron, M., Newman, C. M., & Sidoravicius, V. (2012). Absence of site percolation at criticality in Z

^{2}x {0,1}.*arXiv*, [1211.4138].