Limit theorems for random point measures generated by cooperative sequential adsorption

We consider a finite sequence of random points in a finite domain of finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to the model of cooperative sequential adsorption. The main peculiarity of the model is that the probability distribution of any point depends on previously allocated points. We assume that the dependence vanishes as the concentration of points tends to infinity. Under this assumption the law of large numbers, Poisson approximation and the central limit theorem are proved for the generated sequence of random point measures.