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Percolation on Finite Cayley Graphs

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

Abstract

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 .

Keywords

Abelian Group Simple Group Random Graph Cayley Graph Nilpotent Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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