ON A CLASS OF GROWTH-MAXIMAL HARDCORE PROCESSES

摘要

Generalizing the well-known lilypond model, we introduce a growth-maximal hardcore model based on a space-time point process ψ of convex particles. Using a purely deterministic algorithm, we prove under fairly general assumptions that the model exists and is uniquely determined by ψ. Under an additional stationarity assumption, we show that the model does not percolate. Our model generalizes the lilypond model considerably even if all grains are born at the same time. In that case and under a Poisson assumption, we prove a central limit theorem in a large volume scenario.