Preferencial growth: exact solution of the time dependent distributions
L. Kullmann, J. Kertesz
Abstract
We consider a preferential growth model where particles are added one by one to the system consisting of clusters of particles. A new particle can either form a new cluster (with probability q) or join an already existing cluster with a probability proportional to the size thereof. We calculate exactly the probability i(k,t) that the size of the i-th cluster at time t is k. We analyze the asymptotics, the scaling properties of the size distribution and of the mean size as well as the relation of our system to recent network models.
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