Preferential growth: solution and application to modeling stock market

We consider a preferential growth model where particles are added one by on e to the system consisting of clusters of particles, A new particle can eit her form a new cluster (with probability q) or join an already existing clu ster with a probability proportional to the size thereof We calculate exact ly the probability P-i(k,t) that the size of the ith cluster at time t is k . We applied our model as a background for a microscopic economic model. (C ) 2001 Elsevier Science B.V. All rights reserved.