Karlin, Samuel et Leung, Ming-ying, Some Limit Theorems on Distributional Patterns of Balls in Urns, Annals of applied probability , 1(4), 1991, pp. 513-538
In an independent, equiprobable allocation urn model, there are various Poisson and normal limit laws for the occupancy of single urns. Applying the Chen-Stein method, we obtain Poisson, compound Poisson and multivariate Poisson limit laws, together with estimates of their rates of convergence, for the number of chunks of . (fixed) adjacent urns occupied by certain numbers of balls distributed in some specified patterns. Several related results on occupancy, waiting time and spacings at certain random times are also presented.