Abstract:
We consider random processes occurring on bond percolation clusters and
represented as a generalization of the “divide and color model” introduced
by Häggström in 2001. We investigate the asymptotic behaviors for bond
percolation clusters with uncorrelated weights. For subcritical and
supercritical phases, we prove the law of large numbers and central limit
theorems in the models corresponding to the so-called quenched and annealed
probabilities.
Keywords:percolation cluster, law of large numbers, central limit theorem.