TY - JOUR

T1 - Preferential growth

T2 - Exact solution of the time-dependent distributions

AU - Kullmann, L.

AU - Kertész, J.

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035335440&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.63.051112

DO - 10.1103/PhysRevE.63.051112

M3 - Article

AN - SCOPUS:0035335440

SN - 1063-651X

VL - 63

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 5

ER -