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 -