Abstract
We present analytical and numerical results for the probability distributions of the number of sitesS as a function of the number of shellsl 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 isP(S¦l)~(S/l 4)exp(- aS/l 2) for S≫l≫1.
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Havlin, S., Kiefer, J.E., Leyvraz, F. et al. Probability distribution for percolation clusters generated on a cayley tree at criticality. J Stat Phys 47, 173–184 (1987). https://doi.org/10.1007/BF01009040
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DOI: https://doi.org/10.1007/BF01009040