Statistics of small clusters in system with rare aggregation centers

An integral equation describing the statistics of small clusters in a system with rare aggregation centers is considered in this paper. This equation is obtained from the probabilistic consideration of transition to cluster-cluster aggregation in the small-cluster system. Several different dependences for the characteristic probability are used. A new form of dependence for the cluster-size distribution is obtained. The fluctuation character of used model is discussed. In the case of Poisson's statistics of growth centers, the Levy cluster-size distribution is obtained.