Percolation as a dynamical phenomenon

We consider a percolation process where the probability p of having one site (or bond) occupied increases linearly with time. We study the total number of clusters as a function of time or p, the statistical distribution of jumps in the size of the major cluster, as well as the frequency of these jumps. We find that both distributions are power-laws, with different exponents below and above percolation threshold and we discuss these results.