Preferencial growth: exact solution of the time dependent distributions

Details Preferencial growth: exact solution of the time dependent distributions Preferencial growth: exact solution of the time dependent distributions

2000-12-21

arxiv.org/abs/cond-mat/0012410v1

Physics

Condensed Matter

Statistical Mechanics

8 pages, 4 figures

Scientific paper

10.1103/PhysRevE.63.051112

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 $\Pm_i(k,t)$ 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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