The clustering problem : some Monte Carlo results

I present a series of statistical results on the distribution of the size (i.e. the number of atoms) of clusters formed by atoms scattered randomly in a continuous medium of two or three dimensions. If the range at which they interact is r0, the critical densities (at which infinite clusters appear) are probably of 2.7 ± 0.1 atoms /sphere of radius r 0 (in 3 dimensions) and 4.4 ± 0.2 atoms/disc of radius r0 (in 2 dimensions).