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 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