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Cluster formation in stochastic disk systems
The problem of randomly distributed disks is considered in the dilute regime in a two-dimensional domain. Disks are allowed to overlap and to form clusters which may be isolated or percolating. Depending on the number and size of the disks, distribution functions are obtained for different size and bond configurations of clusters. A statistical geometrical approach is taken to derive analytical probabilities for cluster formation in systems, where a maximum of four overlapping disks is considered. Monte Carlo computations are carried out to verify our theoretical approach which is shown to be in close agreement with numerical simulations.