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 language | English |
---|---|
Pages (from-to) | 173-184 |
Number of pages | 12 |
Journal | Journal of Statistical Physics |
Volume | 47 |
Issue number | 1-2 |
DOIs | |
State | Published - Apr 1987 |
Keywords
- Random walks
- random media
- scaling behavior