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The paper centres on the evaluation of the function n(theta)=N(theta)/N0,that is the normalized number of islands as a function of coverage 0<theta<1,given N0 initial nucleation centres (dots) having any degree of spatialcorrelation. A mean field approach has been employed: the islands have the samesize at any coverage. In particular, as far as the random distribution of dotsis concerned, the problem has been solved by considering the contribution ofbinary collisions between islands only. With regard to correlated dots, wegeneralize a method previously applied to the random case only. In passing, wehave made use of the exclusion probability reported in [S. Torquato, B. Lu, J.Rubinstein, Phys.Rev.A 41, 2059 (1990)], for determining the kinetics ofsurface coverage in the case of correlated dots, improving our previouscalculation [M. Tomellini, M. Fanfoni, M. Volpe Phys. Rev.B 62, 11300, (2000)].Comment: 10 pages, 3 figure

Kinetics of island density in thin film growth in the framework of statistical mechanics of rigid disks