English

Preferencial growth: exact solution of the time dependent distributions

Statistical Mechanics 2009-10-31 v1

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 \Pmi(k,t)\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.

Keywords

Cite

@article{arxiv.cond-mat/0012410,
  title  = {Preferencial growth: exact solution of the time dependent distributions},
  author = {L. Kullmann and J. Kertesz},
  journal= {arXiv preprint arXiv:cond-mat/0012410},
  year   = {2009}
}

Comments

8 pages, 4 figures