A CENTRAL-LIMIT-THEOREM FOR LINEAR KOLMOGOROVS BIRTH-GROWTH MODELS

A Poisson process in space-time is used to generate a linear Kolmogoro v's birth-growth model. Points start to form on [0,L] at time zero. Ea ch newly formed point initiates two bidirectional moving frontiers of constant speed. New points continue to form on not-yet passed over par ts of [0,L]. The whole interval will eventually be passed over by the moving frontiers. Let N-L be the total number of points formed. Quine and Robinson (1990) showed that if the Poisson process is homogeneous in space-time, the distribution of (N-L - E[N-L])/root var[N-L] conver ges weakly to the standard normal distribution. In this paper a simple r argument is presented to prove this asymptotic normality of N-L for a more general class of linear Kolmogorov's birth-growth models.