Modelling Random Linear Nucleation and Growth by a Markov Chain

In an attempt to investigate the adequacy of the normal approximation for the number of nuclei in certain growth/coverage models, we consider a Markov chain which has properties in common with related continuous-time Markov processes (as well as being of interest in its own right). We establish that the rate of convergence to normality for the number of \drops" during times 1; 2; : : : ; n is of the optimal \Berry-Esseen" form, as n ! 1. We also establish a law of the iterated logarithm and a functional central limit theorem.