Absence of Site Percolation at Criticality in Z(2) x {0,1}

作者：Damron Michael^*; Newman Charles M; Sidoravicius Vladas

来源：Random Structures and Algorithms, 2015, 47(2): 328-340.

DOI：10.1002/rsa.20544

• critical percolation
• slab percolation
• sandwich percolation
• two dimensions

In this note we consider site percolation on a two dimensional sandwich of thickness two, the graph Z2x{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.

• 出版日期2015-9