# Geometry and Topology of the Boolean Model on a Stationary Point Processes : A Brief Survey

### Abstract

We shall review some of the author's recent results concerning geometric and topological features of the boolean model on a stationary point processes. While study of geometric features of the Poisson boolean model span a very rich literature, the literature

for topological features of the Poisson boolean model is very nascent and that for a general stationary point process is very little. In particular, the focus will be on asymptotics of geometric or topological statistics of the boolean model on a stationary point process. We

shall mainly give details about topological phase transitions and central limit theorem for geometric and topological statistics.

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