Preferential growth: Exact solution of the time-dependent distributions

L. Kullmann, J. Kertész

Research output: Contribution to journalArticlepeer-review

Abstract (may include machine translation)

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 (Formula presented) or join an already existing cluster with a probability proportional to the size thereof. We calculate exactly the probability (Formula presented) that the size of the (Formula presented) 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.

Original languageEnglish
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume63
Issue number5
DOIs
StatePublished - 2001
Externally publishedYes

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