Probability distribution for percolation clusters generated on a cayley tree at criticality

S. Havlin, J. E. Kiefer, F. Leyvraz, G. H. Weiss

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7 Scopus citations

Abstract

We present analytical and numerical results for the probability distributions of the number of sites S as a function of the number of shells l for several ensembles of percolation clusters generated on a Cayley tree at criticality. We find that for the incipient infinite percolation cluster the probability distribution is P(S|l)~(S/l4)exp (- aS/l2) for S≫l≫1.

Original languageEnglish
Pages (from-to)173-184
Number of pages12
JournalJournal of Statistical Physics
Volume47
Issue number1-2
DOIs
StatePublished - Apr 1987

Keywords

  • Random walks
  • random media
  • scaling behavior

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