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

  • D Yogeshwaran Indian Statistical Institute, Bangalore
Keywords: Boolean model, stationary point processes, topological phase transitions, central limit theorem, intrinsic volumes, Betti numbers.


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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