Percolation on Finite Cayley Graphs

  • Christopher Malon
  • Igor Pak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2483)


In this paper, we study percolation on finite Cayley graphs. A conjecture of Benjamini says that the critical percolation p c of such a graph can be bounded away from one, for any Cayley graph satisfying a certain diameter condition. We prove Benjamini’s conjecture for some special classes of groups. We also establish a reduction theorem, which allows us to build Cayley graphs for large groups without increasing p c .


Abelian Group Simple Group Random Graph Cayley Graph Nilpotent Group 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Christopher Malon
    • 1
  • Igor Pak
    • 1
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

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