Preferential growth: Solution and application to modeling stock market
arXiv:cond-mat/0105473 · doi:10.1016/S0378-4371(01)00286-2
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 P_i(k,t) that the size of the i-th cluster at time t is k. We applied our model as a background for a microscopic economic model.
7 pages, 4 figures, (submitted to Physica A)