Abstract
In this note we consider site percolation on a two dimensional sandwich of thickness two, the graph Z2×{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. "Note added in proof: This extension has recently been accomplished in arXiv 1401.7130."
Original language | English (US) |
---|---|
Pages (from-to) | 328-340 |
Number of pages | 13 |
Journal | Random Structures and Algorithms |
Volume | 47 |
Issue number | 2 |
DOIs | |
State | Published - Sep 1 2015 |
Keywords
- Critical percolation
- Sandwich percolation
- Slab percolation
- Two dimensions
ASJC Scopus subject areas
- Software
- General Mathematics
- Computer Graphics and Computer-Aided Design
- Applied Mathematics