Central limit theorem for germination-growth models in ℝ d with non-Poisson locations

Seeds are randomly scattered in ℝ d according to an m-dependent point process. Each seed has its own potential germination time. From each seed that succeeds in germinating, a spherical inhibited region grows to prohibit germination of any seed with later potential germination time. We show that under certain conditions on the distribution of the potential germination time, the number of germinated seeds in a large region has an asymptotic normal distribution.