Absence of site percolation at criticality in Z2×{0,1}

Michael Damron, Charles Newman, Vladas Sidoravicius

Research output: Contribution to journalArticle

Abstract

In this note we consider site percolation on a two dimensional sandwich of thickness two, the graph Z<sup>2</sup>×{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 languageEnglish (US)
Pages (from-to)328-340
Number of pages13
JournalRandom Structures and Algorithms
Volume47
Issue number2
DOIs
StatePublished - Sep 1 2015

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Sandwich
Criticality
Boundary conditions
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Critical point
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Keywords

  • Critical percolation
  • Sandwich percolation
  • Slab percolation
  • Two dimensions

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Mathematics(all)
  • Applied Mathematics

Cite this

Absence of site percolation at criticality in Z2×{0,1}. / Damron, Michael; Newman, Charles; Sidoravicius, Vladas.

In: Random Structures and Algorithms, Vol. 47, No. 2, 01.09.2015, p. 328-340.

Research output: Contribution to journalArticle

Damron, Michael ; Newman, Charles ; Sidoravicius, Vladas. / Absence of site percolation at criticality in Z2×{0,1}. In: Random Structures and Algorithms. 2015 ; Vol. 47, No. 2. pp. 328-340.
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