On a class of growth-maximal hard-core processes

TL;DR

This paper introduces a generalized growth-maximal hard-core process based on convex particles, proving existence, uniqueness, and non-percolation, and establishes a central limit theorem under certain conditions.

Contribution

It extends the lilypond model to convex particles with a deterministic algorithm, providing new theoretical results on existence, uniqueness, and statistical properties.

Findings

Model exists and is unique under general assumptions.

Model does not percolate under stationarity.

Proves a central limit theorem for large volume scenarios.

Abstract

Generalizing the well-known lilypond model we introduce a growth-maximal hard-core model based on a space-time point process of convex particles. Using a purely deterministic algorithm we prove under fairly general assumptions that the model exists and is uniquely determined by the point process. 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.