Percolation of the Vacant Set

  • Alexander Drewitz
  • Balázs Ráth
  • Artëm Sapozhnikov
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


In this chapter we discuss basic geometric properties of the vacant set \({\mathcal{V}}^{u}\) defined in (5.2.4). We view this set as a subgraph of \({\mathbb{Z}}^{d}\) with edges drawn between any pair of vertices \(x,y \in {\mathcal{V}}^{u}\) with | xy |1 = 1.


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Alexander Drewitz
    • 1
  • Balázs Ráth
    • 2
  • Artëm Sapozhnikov
    • 3
  1. 1.Department of MathematicsColumbia UniversityNew York CityUSA
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  3. 3.Max-Planck Institute of Mathematics in the SciencesLeipzigGermany

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