JournalsrmiVol. 26, No. 2pp. 529–550

On the cluster size distribution for percolation on some general graphs

  • Antar Bandyopadhyay

    Indian Statistical Institute, New Delhi, India
  • Jeffrey E. Steif

    Chalmers University of Technology, Gothenburg, Sweden
  • Ádám Timár

    Universität Bonn, Germany
On the cluster size distribution for percolation on some general graphs cover
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Abstract

We show that for any Cayley graph, the probability (at any pp) that the cluster of the origin has size nn decays at a well-defined exponential rate (possibly 0). For general graphs, we relate this rate being positive in the supercritical regime with the amenability/nonamenability of the underlying graph.

Cite this article

Antar Bandyopadhyay, Jeffrey E. Steif, Ádám Timár, On the cluster size distribution for percolation on some general graphs. Rev. Mat. Iberoam. 26 (2010), no. 2, pp. 529–550

DOI 10.4171/RMI/608