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Percolation on Finite Cayley Graphs

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Randomization and Approximation Techniques in Computer Science (RANDOM 2002)

Part of the book series: Lecture Notes in Computer Science ((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 .

NSF Graduate Research Fellow

Partially supported by an NSF Grant

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Author information

Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Christopher Malon & Igor Pak

Authors
  1. Christopher Malon
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  2. Igor Pak
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Editor information

Editors and Affiliations

  1. Centre Universitaire d’Informatique, University of Geneva, 24, Rue Général Dufour, 1211, Genéve 4, Switzerland

    José D. P. Rolim

  2. Harvard University, DEAS, Maxwell Dworkin 337, 33 Oxford Street, Cambridge, MA, 02138, USA

    Salil Vadhan

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© 2002 Springer-Verlag Berlin Heidelberg

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Malon, C., Pak, I. (2002). Percolation on Finite Cayley Graphs. In: Rolim, J.D.P., Vadhan, S. (eds) Randomization and Approximation Techniques in Computer Science. RANDOM 2002. Lecture Notes in Computer Science, vol 2483. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45726-7_8

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  • DOI: https://doi.org/10.1007/3-540-45726-7_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44147-2

  • Online ISBN: 978-3-540-45726-8

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